The England international's current deal expires in the summer and despite being the side's top scorer so far this season, he has refused to reaffirm his commitment to the club amidst disputes over salary and his desire to play as a striker rather than his nominal right-wing position under Arsene Wenger.
With the January transfer window approaching, there are fears that Walcott - who has been given an opportunity to play in his preferred position in Arsenal's last two matches - could be sold to the highest bidder in order to avoid him leaving the club for nothing at the end of the season.
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"Everyone at the club wants Theo to re-sign," Wilshere told reporters.
"But that is something he has to sort out, it is up to him and the club if they can reach an agreement and I hope they do.
"Theo's been great for us. We just signed five British boys so hopefully he can be the sixth and cap it off. I'm always winding him up, saying, 'C'mon Theo, sign'. It's up to him and the club.
"Theo knows what he means to us and what he means to the fans."
The 20-year-old added that he hoped the decision of he and the four other Brits to commit their long-term futures to Arsenal would help persuade Walcott to tie his own to the club.
"I think he [Walcott] looked at that," continued Wilshere.
"We're all great friends, the British boys, we all go out together, we have meals together and sit together when we're on the road. So hopefully he can follow us and sign."