Walcott scored Arsenal's final goal in their 5-2 win over Spurs playing in his favoured position.
Team-mate Wilshere said: "That is up to him, the boss and the board. I hope he signs. We all know what Theo brings to the team.
"He has pace, he can go behind and his movement and timing of the runs is probably the best around.
"So he can play anywhere - up front, right, left, central. He wants to play down the middle, so I think he will get his chance. He will just have to be patient."