... Gareth Southgate and Glenn Hoddle to lead England in the wake of their "clueless and embarrassing" Euro 2016 exit.
Roy Hodgson stepped down after their elimination at the last-16 stage following the woeful 2-1 defeat to Iceland in Nice.
The Football Association will aim to appoint Hodgson's successor quickly, with current Under-21s manager Southgate the early favourite.
FA chief executive Martin Glenn was due to hold a press conference at England's Chantilly base at 5pm local time (4pm BST) in the wake of England's latest tournament turmoil.
Shearer, who said he would be interested in the role but thinks he "hasn't got a cat in hell's chance" of getting it, believes Hoddle, who managed England at the 1998 World Cup finals, should also return to the fray.
The former Three Lions striker told BBC 5Live: "It was pretty pathetic in my opinion. There was a lot of hype coming into the tournament about our young, energetic youngsters, our players aren't as good as we think they are.
"It was awful to watch, we were clueless. We were out-fought, out-battled, their tactics were better than ours and everywhere you looked on the pitch it was pretty embarrassing.
"He (Southgate) fits their remit, he has been with the Under-21s, he has been around the squad so I would back Gareth Southgate if he was to go in there. But I would also look at getting experience around him like Glenn Hoddle.
"Glenn was brilliant as a coach for England in my opinion, he has got so much to offer and is still young enough so I would totally back Gareth and Glenn."
Shearer admitted he had spoken to the FA several years ago about getting involved in the national set-up and would be keen for further talks this time around, though does not fancy his chances.
He added: "Let's be honest I haven't got a cat in hell's chance of getting it because I don't fit the FA's remit, I haven't got the experience, which I don't believe is right, I haven't got the coaching badges, which I don't believe is right and that is my honest opinion.
"I spoke to the FA a few years ago and got my answer but if they want to speak to me then of course I would."
On England's performance on Monday night, the former Newcastle boss added: "That was the worst performance I've ever seen from an England team. Ever.
"We were out-fought, out-thought, out-battled and totally hopeless for 90 minutes. I said after the three group games that England weren't good enough - I didn't see enough.
"It looked to me like Roy was making it up as he was going along. It was tactically inept.
"How can he pick Arsenal midfielder Jack Wilshere? We had players in the squad who didn't deserve to be there. Manchester City's winger Raheem Sterling hasn't performed. We can go on and on. Then there was Tottenham striker Harry Kane on corners - the list is endless.
"Our players caved tonight. We've all played under pressure, they caved and the manager caved. He gave Manchester United teenage striker Marcus Rashford four minutes and he still did more than anyone else.
"We are blinded by the Premier League, we think it's the best in the world for talent, it's not. We are totally reliant for foreign players and managers for excitement. We are not as good as we think we are."
Harry Redknapp, who was considered for the job when Hodgson was appointed, believes Hoddle is "perfect" for the job.
The 58-year-old was sacked by the FA in 1999 after controversial comments about the disabled, but his reputation as a coach remains intact.
Redknapp said on talkSPORT: "Glenn is your man. Why is Gareth the favourite and more suited?
"I think we have got the perfect man, Glenn fits the bill for me. He said something, but that was a long time ago. He deserves another chance."
On his own prospects of getting the job, he added: "I have got no chance. I don't fit the bill for them. The game is being run by academics. Dan Ashworth will choose the next manager again, maybe there's someone at West Brom we can get in again."
Former England and Tottenham midfielder Jermaine Jenas felt finding the right successor for Hodgson would prove difficult for the FA.
Jenas admitted on BBC5 Live: "I don't know where we go from here.
"Do you want to find a manager who plays a really attractive style of football and gets us playing free-flowing football or do you want someone who has a firm hand, is stronger and makes the decisions at the right time?
"The problem that the FA have got is there a group of managers (in England) who have just stepped into posts. So we are going to be forced down a certain road and what that road is I don't know."
Jenas said England's shock defeat was a combination of poor performances both on and off the field.
"It was a mixture of players massively under-performing, management and a team of staff not being able to make the big decisions at the right time and that includes before the game.
"In the end I think it is Roy's loyalty (to certain players) that has cost him his job and cost England our place in this competition.
"We looked like we didn't have a clue in terms of a way to play. We seem to be still searching for our best team, our best way of playing."
Fellow former England internationals Ian Wright, Lee Dixon and Peter Crouch believe Hodgson's decision to resign as manager was the right one.
Dixon told ITV: "He's done the right thing. From his point of view, but also the team's point of view. He couldn't have taken the team any further.
"He's a lovely guy, honourable. (But) from a coaching point of view, there were glaring errors there from the set-pieces, etc, which weren't taken care of.
"It was just abject. There was no organisation, there was no speed, the organisation of letting a goal in from a throw-in: there was little attention to detail."
Wright added: "It was an abject performance from the boys, but the preparation in what Iceland do was pretty obvious. We were found wanting in that respect.
"(Hodgson) said 'They've been fantastic', which is a nice thing to say, but they've not been fantastic."
Crouch said: "Hopefully people will start talking about him (Hodgson) leaving rather than the performance, and I think that's why he came in and did it so early.
"I don't think there's a fundamental fault (with English players), I think it boils down to pressure."
Former England manager Glenn Hoddle said: "I'm not surprised. He did it with dignity. It's the right timing, with his contract coming to an end, and the way we played in this game.
"It was very lacklustre, there was no movement, not enough options on the ball. Iceland deserved their win."
Another former Three Lions boss, Steve McClaren, told Sky Sports News: "They've not been good enough tonight, not at all. The repercussions of this are going to be absolutely enormous."
Former Liverpool and England defender Jamie Carragher added: "It was a shambolic performance, especially second half. Obviously it didn't go right for us in the first half - that's where the mistakes were for the two goals.
"But for the group of players to not have any sort of clue what to do on the pitch in that situation, to completely panic, we didn't have too many chances, people were doing stupid things with the ball...I don't think I can remember a game as bad as that."
Former England winger Chris Waddle told BBC Radio Five Live: "We haven't got leaders. They're all pampered, they're all just headphones, they don't communicate, on the pitch or off the pitch, you can't get anything out of them. That's why we're no good."
On Hodgson's successor, ex-England striker Alan Smith told Sky Sports News: "I don't think there's an obvious candidate and that's a problem for the FA as I don't think they want to go down the road of a foreign manager again and I don't want them to.
"I think there are only three or four English managers in the Premier League with Sean Dyche coming up to join the other three so it's a big problem for the FA."