The Spain international is back at Stamford Bridge after his mixed loan spell at Real Madrid in the 2023-24 season, where he arrived late in the summer transfer window after Thibaut Courtois's ACL injury.
Kepa initially earned Carlo Ancelotti's trust in between the posts, but he was soon outshone by Andriy Lunin, who was favoured as Courtois's deputy for the second half of the campaign.
Lunin's emergence restricted Kepa to just 20 appearances in a Real Madrid shirt, during which time he kept nine clean sheets, but he has seldom been seen on the pitch since the turn of the year.
The former Athletic Bilbao man did not play a single minute in the Champions League knockout rounds, while he was also overlooked for the Supercopa de Espana final and played in just three La Liga games from January onwards.
Kepa talks 'continue' despite rejected bid
While on the books at the Bernabeu, Kepa expressed his desire to sign for the Champions League and La Liga holders permanently, but with Courtois back at full fitness and Lunin potentially staying on, he may have been third choice next season.
As a result, the 29-year-old returned to Stamford Bridge - where the goalkeeping situation is still clouded in uncertainty - but his deal only runs for another year with no extension in sight.
A permanent move away from Chelsea is therefore expected to materialise in the coming weeks, but according to The Athletic, the Blues have rejected an opening offer from Saudi giants Al-Ittihad.
While the Middle Eastern powerhouses have been knocked back once, the report adds that talks are still ongoing, but they are not alone in their pursuit as other unnamed interested parties are also keeping tabs on the situation.
Moving to Al-Ittihad would see Kepa reunite with ex-Chelsea midfielder N'Golo Kante, who has been rolling back the years for France at Euro 2024, while Karim Benzema and Fabinho are also on the books with the 2022-23 Saudi Pro League champions.
Still holding the honour of being the most expensive goalkeeper of all time, the €80m (£67.3m) man has kept 59 clean sheets in 163 appearances for Chelsea since joining from Athletic Bilbao for that world-record fee in 2018.
Could Kepa still have a future at Chelsea?
Prior to his dream move to Real Madrid - albeit a temporary one - Kepa did force his way back into the Blues XI under Graham Potter and Frank Lampard in the 2022-23 season, capitalising on Edouard Mendy's decline.
While Mendy made the permanent switch to Saudi Arabia, the arrivals of Robert Sanchez and Djordje Petrovic bumped Kepa back down the pecking order, but neither managed to become Mauricio Pochettino's undisputed number one.
A serious injury did not help Sanchez's cause, and it remains to be seen what Enzo Maresca makes of Chelsea's goalkeeping situation, but the uncertainty offers Kepa slight hope that he could reignite his Blues career.
However, Chelsea are instead thought to be perusing the market for new blood, and as Kepa is now in the final 12 months of his contract, a departure is still seen as the most likely outcome.