Manager Andre Villas-Boas last week claimed the striker had indicated he wished to leave the club when his contract expires next summer.
Anelka turns 33 in March and his future at Chelsea looked under threat when former boss Carlo Ancelotti was sacked at the end of last season.
Former France striker Anelka, who has impressed under Villas-Boas, told the club's official website, www.chelseafc.com: "I am linked everywhere but, when you are linked, it doesn't mean you want to leave.
"I like Chelsea and first of all wanted to stay - that's why I am still here.
"I will see what happens in December and, if I am still here, I will see what happens in June.
"I am happy here, I like the club, everyone here, and, after, I will see what happens. It is not only down to me.
"I have been here almost four years now, and I am pleased with the way it has been. It could have been even better but I am still happy."
Villas-Boas also said last week that the club would make efforts to convince Anelka to extend his deal.
The Chelsea boss has been at pains to play down concerns about the age of some of his players but Anelka admitted he was made to "feel old" when he discovered new 18-year-old team-mate Romelu Lukaku used to have a poster of him on his bedroom wall.
He added: "I feel very old. Two or three weeks ago, I went to Paris and saw two kids.
"I was with my friend and we were talking, and they didn't know I used to play for Arsenal!
"They never knew or saw videos, so I was upset, and said I must be very, very old now!"