The 22-year-old endured an injury-hit first season at Stamford Bridge following an €80.4m (£68.7m) move from Leicester City in 2022, making just 20 appearances for the Blues.
Fofana came up with two goals in that time - one in the Premier League and one in the Champions League - as Chelsea suffered a dismal 12th-placed finish in the top flight.
After recovering from a serious knee problem, Fofana became a regular fixture in the heart of the Chelsea defence, but the France international failed to hit the ground running in West London.
Nevertheless, Fofana is still seen as an important part of Chelsea's future, and the defender remains under contract at Stamford Bridge until the end of the 2028-29 campaign.
However, according to Sport1 - via football.london - Bayern were offered the chance to pull off a shock deal for Fofana, who was brought to Chelsea by the German champions' manager Thomas Tuchel.
Bayern are in the market for defensive reinforcements ahead of the 2023-24 season, but the report adds that the Bundesliga giants opted against a move due to Fofana's price tag.
Instead, Bayern are on the brink of signing Napoli centre-back Kim Min-jae, who was linked with Manchester United and Manchester City before Tuchel's side made their move.
Despite only managing 14 Premier League starts in the 2022-23 season, Fofana earned his first cap for the France national team in June, starting in a 3-0 Euro 2024 qualifying win over Gibraltar.
The former Saint-Etienne youngster could benefit from a spate of defensive exits to play a prominent role for Chelsea next season, as Kalidou Koulibaly and Cesar Azpilicueta have sought pastures new.
Koulibaly - who arrived alongside Fofana last summer - has embarked on a new adventure with Al-Hilal, while Azpilicueta has returned to his native Spain with Atletico Madrid.
More defensive outgoings could be on the cards in the coming weeks, as the future of Trevoh Chalobah - who is supposedly wanted by Inter Milan - remains clouded in uncertainty.
It remains to be seen if Ethan Ampadu and Malang Sarr can reignite their Chelsea careers under Mauricio Pochettino too, but the agent of Marc Cucurella has rubbished reports claiming that his client could soon depart.
Goalkeeper Edouard Mendy has followed Koulibaly to Saudi Arabia with Al-Ahli, but Chelsea's outgoings have not been restricted to the defensive third, as midfielders N'Golo Kante, Mateo Kovacic, Ruben Loftus-Cheek, Tiemoue Bakayoko and Mason Mount have all moved on.
Attacker Kai Havertz represents the Blues' biggest sale so far - departing for Arsenal in a £65m move - while Christian Pulisic, Romelu Lukaku, Hakim Ziyech, Pierre-Emerick Aubameyang and Callum Hudson-Odoi are not expected to still be on the books next term.