Arsenal boss Arsene Wenger says he would be open to managing England in the future, but his current focus is with the Gunners.
“One day, if I’m free, why not?” said Wenger, 66, when asked about the role.
The Frenchman celebrates 20 years at Arsenal on 1 October and his contract expires at the end of this season.
The Football Association is searching for a new England boss following Sam Allardyce’s departure after 67 days in the wake of a newspaper investigation.
Allardyce had replaced Roy Hodgson following a disastrous Euro 2016 but left by mutual agreement on Tuesday after the Daily Telegraph claimed he offered advice on how to “get around” rules on player transfers.
Allardyce won his only game in charge of the national team in September – a 1-0 win over Slovakia in the first of their 2018 World Cup qualifiers.
England Under-21 boss Gareth Southgate takes charge of the senior team for the next four matches including three World Cup qualifiers, starting with Malta at Wembley (8 October), Slovenia away (11 October), Scotland at home (11 November) and Spain in a friendly (15 November).
Southgate could be an option for the permanent role depending on his success, while Bournemouth boss Eddie Howe, Crystal Palace manager Alan Pardew and ex-Hull City manager Steve Bruce have also been mentioned as candidates.
Wenger is the longest-serving – and most successful – overseas manager in England, having won 15 trophies during his tenure at Arsenal.
His tally includes winning the Premier League three times and the FA Cup on six occasions.
‘I want to win absolutely everything’
Wenger’s side play Burnley on Sunday at 16:30 BST with his team unbeaten in eight games in all competitions and aiming for a fifth consecutive league victory.
And regardless of speculation over the England role, Wenger says his “priority is to do well here [Arsenal]”.
“It looks like we have moved forward in our game,” he said.
“We have found a good balance between attacking and defending and the team has more belief in what we want to do.”
He added: “I want to win absolutely everything and play the perfect game in every game, that is my dream and get people to enjoy what they see.”
Analysis – the perfect next England manager
BBC chief football writer Phil McNulty
The Arsenal manager’s credentials easily outstrip those of the other candidates being touted as Allardyce’s replacement.
At 66, Wenger might even share Allardyce’s view when he was appointed that his age and experience make him the perfect fit for international management.
Wenger is the perfect next England manager with the ideal credentials and track record if the FA can formulate a plan to somehow attract him to what many now call an impossible job.
