Kepa is believed to be on the verge of a temporary switch to Los Blancos for the 2023-24 season as cover for Thibaut Courtois, who recently suffered a serious ACL injury.
With Edouard Mendy already departing the club for Al-Ahli this summer, and Gabriel Slonina joining Eupen on loan, Kepa's exit would leave Marcus Bettinelli as the only backup to new signing Robert Sanchez.
Bettinelli has also struggled with injuries over the past few months, so Chelsea would inevitably enter the market for a new shot-stopper to act as Sanchez's deputy for the upcoming campaign.
According to The Guardian, Nice shot-stopper and former Premier League winner Schmeichel is on the Blues' radar amid uncertainty over his long-term future with Nice.
Schmeichel ended a successful 11-year spell with Leicester City to join Les Aiglons last summer, leaving with a Premier League, FA Cup and Community Shield winners' medal in his suitcase.
The 36-year-old arrived at the Allianz Riviera as a replacement for Walter Benitez, who joined Dutch giants PSV Eindhoven, and he kept 13 clean sheets from 46 games in his debut season.
Schmeichel quickly established himself as Nice's first-choice goalkeeper over Marcin Bulka, although it has since been suggested by L'Equipe that the latter will start in between the sticks for Nice this season.
Schmeichel supposedly has no interest in playing second fiddle to Bulka this term, and the Chelsea-linked Denmark international could therefore depart the Ligue 1 side this summer.
Nice still have Schmeichel under contract for another two seasons until 2025, but head coach Francesco Farioli will have the final say on the Scandinavian's future.
Despite a largely positive campaign on the field, Schmeichel was at the centre of controversy towards the end of the season amid claims that his casual training schedule was causing friction between him and his teammates.
A separate report from L'Equipe also alleged that Nice players were growing frustrated with Schmeichel's lack of leadership skills, but whether such accusations had any influence in Farioli's decision to make Bulka his new number one is unknown.
Schmeichel previously amassed 83 shut-outs from 284 appearances in the Premier League for Leicester and Manchester City, making eight top-flight appearances for the latter before his departure in 2009.
As well as Sanchez, Chelsea have added Christopher Nkunku, Nicolas Jackson, Axel Disasi, Diego Moreira, Angelo Gabriel and Lesley Ugochukwu to their ranks this summer, and the Blues are thought to be close to reaching a £115m agreement for Brighton & Hove Albion's Moises Caicedo.
Sanchez, Jackson and Disasi could all make their debuts for Chelsea in Sunday's Premier League opener against Liverpool at Stamford Bridge.