Los Blancos have lost Thibaut Courtois to a serious knee problem, with the Belgium international likely to be absent for the entire 2023-24 campaign due to the ACL injury that he suffered in training on Thursday.
Andriy Lunin will start Real Madrid's season opener against Athletic Bilbao on Saturday evening, but the Spanish giants need to bring in another stopper before the end of the transfer window.
David de Gea, who is available on a free transfer following his release from Manchester United, was heavily linked with a move to the club towards the end of last week.
Meanwhile, a deal for Sevilla's Bono was believed to be a possibility, but it has been suggested that a switch for the Morocco international broke down due to the cost involved.
According to AS, Real Madrid have now come to an agreement with Chelsea to loan Kepa for the 2023-24 campaign, but there will not be a purchase option in the deal.
As a result, the Spaniard will return to Stamford Bridge next summer unless a permanent transfer is agreed before then, but Real Madrid will cover his wages for the season.
The report claims that only the minor details need to be addressed, with an announcement on Kepa's move to Bernabeu potentially arriving before the end of the weekend.
Kepa was heavily linked with a move to Real Madrid five years ago, but it is believed that Zinedine Zidane, who was in charge of Los Blancos at the time, blocked the deal.
The 28-year-old became the most expensive goalkeeper in world football when he joined Chelsea from Athletic Bilbao in the summer of 2018.
Kepa has made 163 appearances for the Blues, including 39 outings in all competitions last term, although he has largely struggled to show the type of form that made him one of the most in-demand goalkeepers in world football during his time at Athletic.
The Spaniard will go head-to-head with Lunin for the gloves during the current season, and the Ukrainian was praised by Ancelotti during the Italian's press conference on Friday.
"We give all the confidence in the world to Lunin, who is a great goalkeeper. In the pre-season, he did well. Total confidence in him, we think he is a talent. What he lacks is what everyone lacks, the experience, but he will take it little by little," said Ancelotti.
Providing that there are no late issues, Kepa could potentially make his debut for Real Madrid in their second match of the new La Liga season against Almeria on August 19.