The Frenchman moved to the Blues from Bolton in a £15m transfer in January but has found it difficult to establish himself as first choice in the side.
The 29-year-old has been played out of position on the left wing by Grant and admits it has not been the ideal start to his Chelsea career.
But Anelka insists he is planning to stay for a long time to come.
"Even if I don't always play in the centre that is not so serious. With the number of matches we are playing, there has not been a lot of time to work on my partnership with Didier Drogba.
"Am I keen to play regularly on the left flank? No of course, especially because I have never played on the left before in England.
"People who have worked with me know my qualities are in the centre and I believe the Chelsea coach knows it.
"He uses me alone on the centre or on the flank, but it is not a big trouble to me so far.
"I will be 32 at the end of my Chelsea contract. If they want to keep me, I will stay.
"Otherwise you never know. I can move to the USA or come back to Paris Saint Germain. It is an option I can't exclude."