Redknapp admits it would be "difficult" to make the transition from club boss to international manager.
That hasn't changed the odds (as yet) and Alan Pardew - who has already said "I'm not interested at the moment" - is still out there at 40/1 with Labrokes.
But he must have more of a chance than some of the names on the Labroke's list.
The 'Mackem Leprechaun' at 20/1? God forbid!
As for Alan Shearer at 50/1? What experience has he got - one win in eight games as Newcastle's stand-in boss.
The Tottenham manager has spent the last month dealing with questions about the position, and a number of high-profile managers and players from within English football have backed the 65-year-old to succeed Capello.
Redknapp has blown hot and cold when asked about the job, admitting it is the "ultimate" position for any English manager while also conceding it would be hard to leave Spurs after three and a half years of success.
"I'm not sure," Redknapp said in an interview with L'Equipe when asked if he would like to manage England.
"I have a very good job at Tottenham today and I like it. But I do not know. We will wait and see."
Harry Redknapp 1/4
Roy Hodgson 7/1
Stuart Pearce 8/1
Jose Mourinho 9/1
Josep Guardiola 11/1
Martin O'Neill 20/1
Guus Hiddink 25/1
Arsène Wenger 33/1
Glenn Hoddle 33/1
Gareth Southgate 33/1
Rafa Benitez 33/1
Sam Allardyce 40/1
David Beckham 40/1
Alan Pardew 40/1
Alan Shearer 50/1
Alex Ferguson 50/1
Terry Venables 100/1
Steve McClaren 100/1
Neil Warnock 100/1