The Greek champions want to take the 17-year-old on a two-year loan from the Premier League giants.
Kakuta joined Chelsea in 2007 from Lens and was voted Scholar of the Year in his first season with the Blues.
The French youth international, who can play in midfield or attack, is highly rated and there is no suggestion Chelsea would contemplate selling him.
But former Chelsea scout Pelle Andersson is reported to have tipped off Olympiakos about Kakuta's potential.
However, reports suggest that Olympiakos' initial approach has been rebuffed as Chelsea want him to stay and develop in West London.
Kakuta is currently recovering from a broken ankle and is not due to return until the summer.