The Spain international became the most expensive goalkeeper of all time when he moved to Stamford Bridge from Athletic Bilbao for £72m in 2018.
The 27-year-old has largely struggled to make his mark with the Blues, though, and is currently second choice at the Premier League club behind Edouard Mendy.
Kepa, who has made 13 appearances in all competitions at club level this season, still has over three years left to run on his contract with Chelsea.
The report claims that the offer of a loan with an obligation to buy could also be considered by the European Cup holders.
Kepa has made 122 appearances for Chelsea since arriving from Spanish football, and he had a spell in the team last month due to Mendy's involvement in the Africa Cup of Nations. body check tags ::