Tottenham will try and tempt Gareth Southgate to leave the England national side to become their new manager should Mauricio Pochettino walk away from the club.
The Argentine hinted that his future may lie elsewhere in the summer, amid frustration around his lack of control over transfers.
The 47-year-old suggested the club change the title of his job from manager to head-coach during pre-season, which could influence his plans for the future.
The Daily Star have now claimed that Southgate would be Levy’s first-choice successor to the Pochettino, despite his contract with England.
The former Middlesbrough defender’s current agreement lasts until the culmination of the 2022 World Cup, four years after he guided his country into the last four in Russia.
However, the 2020 European Championship, which will in part take place in London, could have an effect over his position, and may affect the strength of his relationship with the FA.
The English core at Tottenham of Harry Kane, Dele Alli, Eric Dier, Danny Rose and Harry Winks could prove to help Southgate transition back into club football, after a mixed spell at the Riverside between 2006 and 2009.
The report goes on to claim that a poor result against Bayern Munich on Tuesday will add to the pressure on Pochettino after their defeat to Colchester on penalties last Wednesday, despite a battling win over Southampton.
When asked why he does not look as buoyant earlier in the season, Pochettino said: “It’s not like this. I explain why – in football I suffered two big disappointments.
“One when I was a player and there was the penalty at the World Cup. It was always my dream to play in a World Cup, my massive, big dream. OK, we played three games and went home.
“We went there unbeaten, a candidate to win the trophy and went home in the Group stage. I stayed at home and didn’t go out for 10 days.
“Another day was with Tottenham to win a trophy and the closest to win a trophy was of course the Champions League and it was made even bigger because it was the Champions League.
“To achieve the final of the Champions League with Tottenham – no-one expected that. It was more than a dream, more than a dream.
“In that moment I felt disappointed and then I took a train, after the train, to Barcelona and again you feel like you are depressed.
“In your mind, you expect to move on after a week and say ‘I want to, again, be there.’ You cannot be happy.
“Yes, we have some disagreements, of course. But I am happy now because I am a positive and of course this season is going to another massive challenge. But we must have that energy to try to be contenders and try again to fight for big things and I’m going to try until the end.”