Football Association chief executive Martin Glenn says Arsenal's Arsene Wenger is among the candidates who "fit the criteria perfectly" to succeed Sam Allardyce as England manager.
Allardyce left his post after just 67 days this week, having been secretly filmed by undercover reporters allegedly offering advice on circumventing FA rules governing the transfer of players under third-party ownership.
England's Under-21 coach Gareth Southgate has taken charge of the senior team for the next four matches as a long-term successor to Allardyce is sought.
Wenger, who this month celebrated his 20th anniversary as Gunners boss, is out of contract at the end of the season and has been put forward by some as a possible solution.
"Of course he'd fit the criteria perfectly. Of course he would, as would a few others," Glenn was quoted as saying by the Guardian when asked about Wenger's potential candidacy.
Allardyce meanwhile now faces the prospect of a suspension from the game for breaching FA regulations.
"It could range from a fine to a ban," Glenn said.
"That's what the history shows. That's for a tribunal to decide."
The FA chief executive defended the decision to employ a manager whose conduct came under scrutiny during Lord Stevens' inquiry into football corruption in 2006, having also been the subject of an investigative report by BBC current affairs programme Panorama.
"We knew he was a man of the world, we knew there had been a Panorama inquiry a few years ago," Glenn said.
"But he was a guy who had a senior position on the League Managers' Association. Known in the game.
"We referenced him widely. He's Sam, he's loud, he's brash but he is in the middle of the fairway in terms of behaviour. So I think that the reason I felt let down was, I guess, the surprise factor of it.
"He was seen to be a stalwart of the game. Yes he's Sam and he's loud so we did understand that he's not going to be the quietest person.
"But you could not have predicted that behaviour. I take full responsibility for the decision to hire him but I don't take responsibility for his actions."