England manager Gareth Southgate's employers want him to extend his contract beyond the end of the 2020 European Championship.
Southgate's popularity with the fans rocketed last month when England reached the semifinals of the World Cup, where the team was beaten by Croatia.
He was handed a four-year deal by the Football Association in November 2016, after taking over from Sam Allardyce.
"Gareth has been excellent, we'd like him to stay beyond 2020," FA chief executive Martin Glenn said on Wednesday.
"I think we'd both like that but if we talked about it at any length it would then be a contract conversation and he's on holiday now, so we'll talk when he comes back.