Sunderland manager Sam Allardyce
However, Allardyce could face competition from Harry Redknapp, with Dan Ashworth, the country's head of elite development, due to meet with the former Tottenham Hotspur and Queens Park Rangers boss, the report claims.
Ex-QPR boss Harry Redknapp
Allardyce has been with Sunderland for the past nine months and steered them to Premier League survival last season.
However, the 61-year-old is said to have an escape clause in his contract at the Stadium of Light, which expires next summer.
Allardyce kept Sunderland up at Newcastle's expense
Redknapp, on the other hand, has been out of full-time management since February 2015, but has held interim roles with Jordan and Derby County, where he acted as advisor to young head coach Darren Wassall, in the meantime.
The report claims another caretaker role is possible, with the 69-year-old expected to groom a younger coach to succeed him long-term.
Rio Ferdinand, brought through by Redknapp at Upton Park, could be groomed for the role by the 69-year-old
Last week, the same publication reported that Allardyce was keen on the position, which was vacated by Roy Hodgson in the aftermath of England's Euro 2016 quarter-final defeat to Iceland.