The Telegraph says manager Frank Lampard has ruled out signing a new keeper this month but will shell out on a new custodian if Kepa fails to live up to his price-tag between now and the summer.
Willy Caballero will start in goal for Chelsea against Hull in the FA Cup as normal so Kepa, 25, will be able to rest and recuperate ahead of his side's next league clash against Leicester next Saturday.
Lampard, speaking ahead of Chelsea's cup clash at the KC Stadium, said of Kepa: "I am not looking at it now.
"I am not affected by criticism from the outside as much. I am aware of it, not affected by it. It is what I want for the team and I think with Kepa he knows, he'll be honest that there have been some mistakes that have cost us goals. It is the nature of it, so that needs to improve."