Kamara is out of contract at the end of the season and the midfielder is yet to agree to sign a new contract with Marseille.
Marseille are not confident about the Frenchman signing a new deal and are believed to be considering selling him in the winter transfer window.
But Kamara wants to wait until the summer and it has been claimed that he does not want to change clubs this month.
He is looking for a clean exit at the end of the season and, according to French outlet Foot Mercato, Chelsea are amongst the clubs who are in contact with his representative.
The Blues have their eyes on him and are keen to snap him up on a free transfer next summer.
Chelsea will be in the market for a midfielder at the end of the season and Kamara is a target.
However, Barcelona and Bayern Munich are also in the mix for him and have contacted his agent.
Newly rich Newcastle are also firm admirers of Kamara, having had him on their radar for some time, and remain keen on a deal to take him to St James’ Park.