Walcott rejected an offer of a new £75,000-a-week, five-year deal at Arsenal in the summer and as yet there has been no further progress made by the Gunners in regards to extending his stay.
The England international has stated he is keen to play in a central role and insists this is why he is yet to resolve his future at the Emirates.
Walcott's contract situation has alerted a number of clubs and it has been suggested that United have joined the likes of Chelsea, Liverpool, Manchester City and Juventus in the battle for the forward's signature.
It is thought that Nani could be set to depart Old Trafford, either in January or the summer, and boss Sir Alex Ferguson has targeted Walcott as his replacement.
Walcott will be free to sign a pre-contract agreement with a foreign side in January, which may give any European side with an interest in the Gunners forward an advantage.
However, Arsenal may be tempted to sell Walcott in January, rather than lose him for nothing in the summer, and United may make a cut-price offer for the 23-year-old.