Walcott’s current contract expires next summer and the England international has been linked with a move to Premier League rivals including Chelsea and Manchester United.
And, while Vermaelen remains hopeful his team-mate will stay put, he has stressed the team’s other players are in the dark over any on-going discussion.
“Of course we want him to stay but that is something that is going on between the player and the club,” Vermaelen told reporters.
“I don’t know what is going on behind the scenes — we don’t talk about it. Of course, Theo has been invaluable for us when he played this year. He is dangerous for us and I hope he could stay this year.
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“We know his qualities — he is quick and goes in behind defenders all the time — and I think we could find him yesterday and it helped us score a few goals.”
The Gunners put their shock Capital One Cup exit at the hands of Bradford City behind them by beating Reading 5-2 on Monday, and the former Ajax player was delighted with his side's reaction.
He added: “The team were disappointed because, of course, you want to win [against Bradford] but the thing is we were focused straight away again and we know in England we have so many games that we can make it up again straight away,” he said.
“You can’t stand still too long with a defeat like that — you just learn from it and move on.
“We had a lot to prove. A lot of people questioned us, and maybe that’s normal, but we wanted to perform yesterday and we think we did that.”