The 28-year-old is still the world's most expensive keeper after moving from Athletic Bilbao to Stamford Bridge for £72m in the summer of 2018.
Kepa regained his place as first-choice stopper in West London during the 2022-23 term, starting 29 Premier League matches for the Blues as they finished 12th in the final standings.
Over a five-year period, the Spaniard has made 163 appearances for the club, and was part of the side who won the Champions League under Thomas Tuchel in 2021.
According to the Daily Mail, Kepa could be set for a reunion with the German manager, as Chelsea are willing to offload the keeper this summer amid interest from Bayern Munich.
It is understood that the Blues' stance on the former Bilbao man's situation has been altered by the recent arrival of Robert Sanchez from Brighton & Hove Albion for £25m.
Sanchez lost his place in between the sticks for the Seagulls to Jason Steele at the end of the 2022-23 campaign, although that was after the Spaniard expressed his desire to depart from the South Coast.
The Londoners have already allowed Edouard Mendy to leave the club this summer, with the Senegal international securing a lucrative switch to the riches of the Saudi Pro League.
Tuchel is said to be a huge admirer of Kepa despite playing Mendy in front of him for the majority of his tenure at Chelsea, and the pair could be set for a reunion in Germany.
With Manuel Neuer still recovering from a broken leg suffered in December, the Bavarian giants are in the market for a new shot stopper to help them retain the Bundesliga crown next term.
Yann Sommer recently made the switch from Bayern to Serie A outfit Inter Milan, meaning 35-year-old Sven Ulreich is set to start the club's Super Cup clash against RB Leipzig on Saturday.
After Andre Onana moved to Manchester United, Inter needed a new first-choice stopper, and the 2023 Champions League finalists moved decisively to secure the services of the Switzerland international.
Chelsea kick off their Premier League campaign when they welcome Jurgen Klopp's Liverpool to Stamford Bridge on Sunday afternoon, with Mauricio Pochettino aiming for a positive start to his tenure at the Blues.