Conte's future came under the microscope during the summer due to reports of underlying tension between himself and the board with regards to transfers.
The reigning Premier League champions have brought in Antonio Rudiger, Tiemoue Bakayoko and Alvaro Morata to strengthen the team, but they have lost John Terry and Nemanja Matic, while Diego Costa is refusing to return.
Despite the Italian coach signing a new two-year deal in July, Bild has claimed that Chelsea officials have sought out Tuchel about potentially taking over.
The German publication claims that Chelsea director Marina Granovskaia is behind the move for Tuchel after she was left fuming about Conte's treatment of Costa, whom she helped the club sign from Atletico Madrid in 2014.
However, according to The Mirror, the West London outfit have no plans to part with their current manager, who has overseen one defeat and one win so far in the league this season.
Tuchel left Dortmund at the end of the 2016-17 campaign following disputes with a number of senior officials.