The Blues are currently 12 points behind Manchester United and have 17 games left to play.
Anelka admits they will have to win their remaining games in order to have a chance to overhaul United.
“It is going to be tough but anything is possible, even if it is very hard,” he told his club’s official website.
“We have to win every game from now, and maybe we can do it, but to win every game is hard. Most important is to win against the teams that are around and in front of us.
“At Arsenal in 1998, we had belief because, like I said, in football anything is possible, and if you are winning game after game and others are dropping points, it can happen.”