Arsene Wenger has stopped short of ruling himself out of the England running but says he is "completely focused" on Arsenal.
Wenger is inside the final year of his Arsenal deal and has repeatedly said he will not break his contract.
But Gareth Southgate has been put in temporary charge for England's next four games, and there is just one further fixture scheduled before the end of the Premier League season.
Asked after Arsenal's Champions League win over Basel whether he was flattered to be linked with the England job, Wenger said: "Of course, but my priority has always been this club. Until the end of this season I'm here, and I am completely focused on that."
Asked whether he meant he was at Arsenal just until next summer he said: "My priority is always Arsenal and I have to assess how well I do until the end of the season."
Southgate will oversee the upcoming World Cup Qualifiers against Malta and Slovenia, and next month's games against Scotland and Spain, following Sam Allardyce's abrupt departure this week.