The 32-year-old is behind the likes of Didier Drogba and Fernando Torres in the pecking order at Stamford Bridge.
Anelka has a year left on his current contract with the Blues, but wants to leave this month.
Anelka stated earlier this summer that he wanted to stay on at Chelsea to fight for regular first-team football, but the striker is now ready to leave.
Anelka said: “I still have one more year, and I am pleased with the work I’ve done since I came to Chelsea.
“I’m still here. I want to stay on until the end of my contract in one year and after that we will see what happens.
“I have never said I wanted to leave Chelsea. Even if there’s an offer from someone else, I don’t care because I’m seeing out my contract at the club.”