The versatile youngster has spent the past two seasons on loan at Borussia Dortmund, where he has chalked up seven goals and 10 assists in all competitions during the 2019-20 campaign.
Hakimi's contract at the Bernabeu is set to expire in 2022, and his performances for Lucien Favre's side this season have supposedly garnered a significant amount of interest from other clubs.
According to The Mirror, Dortmund do not have the option to sign Hakimi on a permanent basis once his loan deal expires, and Chelsea have allegedly enquired about the 21-year-old's availability.
However, the report also claims that Los Blancos will not make any decisions until the season draws to a close, and the Blues could supposedly face stiff competition from Bayern Munich for Hakimi's signature.
The Morocco international has netted twice in 17 appearances for Zidane's side.