Former Middlesbrough boss Gareth Southgate is favourite to succeed Stuart Pearce as England U21 coach.
Southgate is one of the leading contenders to take over. Peter Taylor and Phil Neville have also been linked with the job, as has ex- England chief Glenn Hoddle, says The Sun.
FA chairman David Bernstein - who retires next month to be replaced by Greg Dyke - refused to speak about Pearce's future.
He said: "That will be discussed after the tournament.
"He has been pretty successful for us but this tournament hasn't been a success.
"Overall, I think he's done well over a long period, particularly with all the factors. He's operated with quite a difficult hand."