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.
Second time lucky for Allardyce?
Allardyce, 61, is currently in Austria, where the Black Cats are preparing for the new season.
He was interviewed for the England job in 2006 following the departure of Sven-Goran Eriksson, but the FA instead chose to appoint Steve McClaren, who had been the Swede’s assistant manager.
He signed a two-year contract with Sunderland in October before steering the club to Premier League safety after suffering only one defeat in their final 11 league matches of the season.
Prior to that he spent four seasons as boss of West Ham, who he led back to the Premier League via the play-offs in 2012.
He has also managed Blackburn, Newcastle, Blackpool, Notts County and Bolton, who were promoted to the top flight and qualified for Europe during his tenure.
Klinsmann to return?
The former striker is well known to English audiences after spending the 1994-95 season in the Premier League with Tottenham.
As a coach, Klinsmann, 51, took Germany to the semi-finals of the 2006 World Cup, held on home soil.
An ill-fated stint in charge of Bayern Munich ended in April 2009 when he was sacked and replaced by Jupp Heynckes.
He took over the US side in 2011 and won the Concacaf Gold Cup in 2013 and reached the last 16 of the 2014 World Cup, where they were beaten by Belgium in extra time.
USA were beaten by Jamaica in the semi-finals of last year’s Gold Cup and reached the semi-finals of last month’s Copa America Centenario, where they lost to Argentina.