Alex Ferguson has been interested in the player and it was said that he would be keeping tabs on him until the summer and then making a move to bring him to Old Trafford as a replacement for Paul Scholes.
But it is said that Eriksen is only interested in staying with Ajax for the immediate future.
The player said: "I think that I'm still developing here at Ajax and that the regular playing time that I am getting is making me better and better.
"I don't see the need for a move at the moment. I feel very much at home here and there is plenty I can still learn."