The Croatian was a key part of the Blues midfield that won the Champions League under Tuchel, but has made just 15 Premier League starts so far this season.
The January signing of Enzo Fernandez for a British-record transfer fee has added to the competition for a place in the XI, while N’Golo Kante is fit again and expected to sign a new deal and the club are also seeking another major midfield addition this summer.
Kovacic is about to enter the final 12 months of his contract and looks likely to leave Stamford Bridge as part of a major clearout, with the club needing to recoup transfer fees and trim a bloated squad after two windows of major spending since Todd Boehly’s takeover.
It is understood that Chelsea would prefer to sell the midfielder to a club outside England if possible.
Tuchel took over as Bayern boss last month, having been sacked by Chelsea in September 2022. The German has been linked with moves for a number of players he worked with at Cobham and is also interested in a move to take Mason Mount to the Allianz Arena.