Arsenal boss Arsene Wenger and Tottenham counterpart Mauricio Pochettino say they are open to managing England in the future.
The Football Association is searching for a new England boss following Sam Allardyce’s departure after 67 days.
Asked about taking the job, Wenger, 66, said: “One day, if I’m free, why not?” Pochettino, 44, said: “Yes, why not? In the future.”
Both said they are committed to their current clubs.
Allardyce, who replaced Roy Hodgson following England’s disappointing Euro 2016, 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, a 1-0 victory over Slovakia in their opening 2018 World Cup qualifier in September.
England Under-21 boss Gareth Southgate will take 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.
Frenchman Wenger is the longest-serving – and most successful – overseas manager in England, having won 15 trophies during his 20-year tenure at Arsenal, including three Premier League titles and six FA Cups.
Arsenal, who are unbeaten in eight games in all competitions this season, play Burnley on Sunday at 16:30 BST aiming for a fifth consecutive Premier League victory.
Pochettino has earned a reputation as one of the brightest managerial talents in English football.
The 44-year-old Argentine led Southampton to eighth spot in the Premier League in 2012-13 before moving to Spurs in 2014.
Last season, he took Tottenham back into the Champions League with automatic qualification from a third-placed league finish.
Burnley boss Sean Dyche, 44, ruled himself out of contention for the England job because of a lack of experience.
“If you want to build a chance of being good at that kind of level, you need more years and layers of experience,” he said.
“In the future, who knows? Maybe. But at the moment I think there are people better placed than me.”
Analysis – ‘Wenger the perfect manager for England’
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.
Subscribe to the BBC Sport newsletter to get our pick of news, features and video sent to your inbox.