Gareth Southgate, the bookmakers' favourite to be the new England manager, does not want the job on a temporary or permanent basis, the BBC is reporting.
England's under-21 manager had been widely tipped to take over on a temporary basis while the Football Association conducted a review of England's failure at Euro 2016 and looked for a permanent successor to Roy Hodgson, who quit on Monday.
But the BBC on Thursday said the England job "is not what Southgate wants at this stage" either on a permanent or temporary basis.
Southgate, however, remains favourite at 5-1 with bookmakers. Former England coach Glenn Hoddle is 11/2 with US coach Juergen Klinsmann at 7/1, coming in from 25/1. Arsenal coach Arsene Wenger is 12/1.
England went out of Euro 2016 in the second round after a 2-1 defeat by Iceland.
Earlier, Football Association (FA) chairman Greg Dyke said it might struggle to convince top managers to take the England coaching job.
A three-man panel of FA staff has begun the job of finding his successor.
Also linked to the job by British media are Bournemouth's Eddie Howe and Hull City's Steve Bruce.
"It's got to be somebody who really knows English football,"said Dyke, whose term ends in July.
"But there's loads of them now, more of them than there are English. The harder question is why anybody would want it.
"They get media pressure that no one else in football gets."
However, David Bernstein, a former FA chairman, backed Sunderland manager Sam Allardyce to succeed Hodgson.
"I'm not saying we should have an English manager. But, of the English managers, I actually would go for Sam Allardyce," Bernstein said.
"He's a very powerful character. I think he's got the personality, the strength, he's a good technical manager, he's very experienced and he's someone who perhaps could imbue confidence."
England next play in a 2018 World Cup qualifier on September 4 away to Slovakia.