Arsene Wenger would “fit the criteria perfectly” of the next England manager, according to Football Association chief executive Martin Glenn.
Arsenal boss Wenger, whose contract is up at the end of the season, has said that he is open to taking on the role.
Glenn added that the FA was not “wedded to the fact he has to be English” in their hunt for a national team boss.
Sam Allardyce left the post on Tuesday after apparently offering advice on getting around player ownership rules.
Allardyce said he is “deeply disappointed” to have left the role and apologised for his comments, which were filmed by undercover Daily Telegraph reporters.
Wenger was appointed as Arsenal manager in 1996 and has won three Premier League titles and six FA Cups during his time at the club.
The 66-year-old will be out of contract in May and is third favourite for the England job behind Gareth Southgate, who will take interim charge for the next four matches, and Leipzig director of sport Ralf Rangnick.
Glenn said Wenger was one of “a few” managers who possessed all the qualities necessary for the role.
“If I am free one day, why not?” Wenger replied when asked about the possibility of taking on the England job on Friday.
Glenn added that Southgate’s caretaker tenure would allow the England Under-21 boss the chance to decide if he wished to be considered for the senior-team role.
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Southgate ruled himself out of the running to replace Roy Hodgson in the wake of the team’s poor showing at Euro 2016.
“I think he is a genuine contender, but this isn’t an audition,” Glenn said of Southgate.
“He has a choice to make at the end of that whether he really wants to throw his hat into the ring, but he wouldn’t be the sole candidate.
“We are not looking for a saint, we are looking for someone who is great at winning matches, can motivate a team, can make us a far better competitor.
“That doesn’t require a saint but it does require someone who understand they are a role model as well.”
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