Arsene Wenger has revealed that the Belgian centre-back is in contention to face Chelsea, while the English midfielder will make his comeback for the Under-21s in the next week
Vermaelen missed the 1-1 draw against Manchester City last weekend, while Wilshere has missed over a year of football following ankle problems.
Arsene Wenger revealed in his press conference ahead of Saturday's game against London rivals Chelsea that the Belgian defender is available again for selection, while Bacary Sagna is back in full training, but will not play against the Blues, while Tomas Rosicky and Wojciech Szczesny are both at least two weeks away from returning.
"If we do well at home against the strong teams it will have a big impact on our chances," Wenger told the club's official website.
"I have selection solutions, not selection problems. You want two players in every position. Rosicky is two weeks away, Szczesny is two or three weeks away."
Wenger also stated that Wilshere will be back to play on Monday night for the Under-21 side, but that he will not feature in the upcoming World Cup qualifiers for England.
He added: "Jack will play on Monday for the [Under-21s]. He will play an hour. We have to be patient. I think that [the England games] will be too early for him."
Wenger also spoke about Saturday's opponents Chelsea, adding that John Terry's recent international retirement was a surprise to him, and that he certainly does not miss Didier Drogba, who left the club in the summer.
"I don't know if Chelsea miss [Drogba], but we don't miss him. He did a lot of damage against us," Wenger added.
"[John Terry's retirement] was a surprise to me. If it's how he feels you have to respect the decision.
"[Chelsea] were efficient [in Europe] They showed tenacity, a bit of luck too, and you have to congratulate them. I am not surprised that [Eden Hazard] has gone to Chelsea and is straight away one of their stars.
"We will know more about us on Saturday afternoon, but much more about us after 10 or 15 games."