Gareth Southgate resigned after defeat in the Euro 2024 final against Spain, since then a permanent manager has not been found for England.
Lee Carsley will remain interim until at least the autumn while the FA finds suitable candidates.
Two sources told the BBC that preliminary talks had been held with German Tuchel.
One source stated advanced discussions were proceeding, and no news was likely on Tuesday, but Tuchel is rapidly becoming the favorite as things could move quickly.
An approach is also made for Manchester City manager Pep Guardiola in the summer to see if had an interest in the England job.
Neither the FA nor Manchester City opted to comment publicly when contacted by BBC Sport.
Tuchel left Bayern Munich in May, when he still had a year on his contract, following the Bundesliga title slip-up for the first time since 2011-12 for the German giants.
He has also previously managed Mainz, Borussia Dortmund, and Paris St-Germain.
The 51-year-old was Chelsea manager from January 2021 until September 2022, winning the Champions League, FIFA Club World Cup, and UEFA Super Cup.
It was Gareth Southgate’s final march, the final time he would pitch under England’s flag after eight years, where only Sir Alf Ramsey, the triumphant manager of England’s 1966 World Cup win, could have walked on for the finals of a major tournament with the England men’s team.
For the 2018 World Cup semi-finals and 2022 World Cup quarter-finals, he led England in four major competitions.
Since taking the job, Carsley has led three wins and one defeat in the Nations League.
Like Southgate, Carsley was previously England Under-21s manager and took the team into the European U21 Championship in 2023.
Following the defeat to Greece, Carsley said he hoped “to go back to the under-21s.”
The 50-year-old, after a victory over Finland, insisted he had “definitely” not ruled himself out of taking over the role on a permanent basis, adding: “England deserves a world-class coach,” and admitted he is “still on that journey.”
Among those previously linked with the permanent vacancy were Newcastle manager Eddie Howe, and former Brighton and Chelsea boss Graham Potter.
