Agent Spencer Downey, who represents the Geordie duo, has confirmed both players are in talks with Magpies manager Alan Pardew about extending their contracts.
Agreements have yet to be struck but by offering the players, both aged 21, new contracts, the St James' Park outfit will now be entitled to compensation should they move on.
Saints boss Danny Lennon is keen to keep Newton and Dummett in Paisley after both played key roles in the team's Scottish Communities League Cup triumph.
While there is also interest from npower Championship sides Bolton, Huddersfield and Doncaster, St Mirren have been told they will not have to come up with a fee if the players decide to stay put in Scotland.
Downey: "Newcastle have offered the lads contract extensions but the talks are on-going. There is still an agreement to be reached on matters like the lengths of the contracts so we will just have to wait and see what happens.
"Nothing has been decided yet and there is interest from other clubs.
"But Newcastle have been impressed by the way Conor and Paul have been treated during their time in Scotland and have agreed that if they do sign for Saints permanently, they will not ask for the compensation fee they are entitled to.
"Instead they will just ask for a sell-on clause to be inserted in their contracts that will see them take a share of any future profit."
Left-back Dummett arrived in Scotland last summer and has made 33 appearances for Saints, while Newton followed in January.
The midfielder has made 17 appearances for Lennon's team and scored his first goal for the club in the 3-2 win over Hearts at Hampden, which secured Saints' first major trophy in 26 years.
Newton: "I haven't accepted the deal from Newcastle yet, we're still talking but I know that other clubs have been on to my agent.
"I owe a lot to St Mirren. It's been a great season for me but nothing has been put down on paper about a permanent move here.
"But it would be an option I'd consider as I've loved my time up here.
"It's still early for me. I would like to test myself down south at some point in my career but I've only been playing first-team football for the past four months so I'm not nave enough to think I'm just going to walk into the side at Newcastle.
"So the next few months are crucial for my development.
"But I would love to make it at Newcastle and get a chance to play in those black and white stripes. It's what every lad from the city dreams of. Right now, though, I will just bide my time."