The England midfielder hopes the club can come to resolution that keeps the former Southampton winger at the club, while he is also happy with the speed of his return from injury
The former Southampton player's contract runs out at the end of the season, and his game time has been limited amongst the uncertainty that surrounds his future.
But Wilshere believes it is imperative that the club's hierarchy manage to conclude a deal to retain Walcott, who helped the Gunners earn a precious point against Schalke on Tuesday night.
"Theo has been great," Wilshere told the Evening Standard.
"His future is down to him and the boss to sort out. I hope he does sign.
"He has been great for us. He's an English lad and great to have around."
Wilshere has only recently returned from injury after nearly 18 months on the sidelines, but picked up a red card against Manchester United that has ruled him out of Arsenal's match against Fulham this weekend.
"I am gutted to miss Fulham after being out for so long," Wilshere continued.
"It's disappointing to miss any game but if I think about it another way, maybe it will be good for me to have a little break and come back for the Tottenham game [a week later].
"It is difficult [to be out for so long] for any player and especially for me — I was 19 and just breaking into the footballing world and coming into the team.
"To have a setback like that was heartbreaking but now I'm back.
"Last night, I felt better than I did over the weekend and the weekend before that, so I am feeling better after each game.
"It's a long season, so I need to take it easy a bit but I am looking forward."