Sunderland manager Sam Allardyce has yet to be contacted by the Football Association about the England job.
It is also understood no official approach has been made to the US Soccer Federation about Jurgen Klinsmann.
This week, it was reported that Allardyce would be interviewed about succeeding Roy Hodgson, who resigned after England's Euro 2016 exit.
It was also claimed Klinsmann has had discussions over the role, with the German thought to be in California.
Bournemouth manager Eddie Howe has also been linked with the job.
Hodgson's successor will be chosen by a three-man panel of FA technical director Dan Ashworth, chief executive Martin Glenn and vice-chairman David Gill.
They have already spoken to former internationals - including Frank Lampard, Rio Ferdinand and Gary Lineker - as part of its review and have not ruled out an interim appointment, with World Cup 2018 qualifying beginning in September.
England Under-21s boss Gareth Southgate has already ruled himself out of the running.