But striker Thierry Henry is in no doubt that he wants Bergkamp to stay.
The Frenchman said: "He fancies playing another year I also fancy him playing for another year. Without saying anything bad about anyone, when Dennis plays, I only concentrate on going behind the defence. When he is not there, I have to drop back.
"I have played with a lot of great players and he is amazing. He always has a great desire when he is on the pitch and you can never complain about him.
"At his age, to be doing what he is doing, it is unbelievable. I don't know if I will still be playing at his age. He is a great guy."
Bergkamp said: "It was so important to get a result against Newcastle. As for the gap between us and Chelsea, you never know. It will be difficult but we try not to look at the table.
"We need to start playing like we used to.
"We can't do anything about Chelsea. We have lost too many points and that is our own fault."
