The England international has been hampered by a problem with his left ankle, for which he underwent a minor procedure in February.
He took a significant step on the road to recovery when he completed a full game in Tuesday's 4-1 win over Stoke City, when Abou Diaby also got some game time.
And now Wilshere, who has not played since the 2-1 loss to Manchester United in November, wants to get involved in Arsenal's bid for Premier League and FA Cup honours.
"You can train as much as you like, but you can't get that match fitness unless you play," he told the club's official website.
"In the Premier League you know how quick it is so you have to get back to that speed.
"I feel like I'm ready to play some part. When you're injured you look at your comeback date and the games around that time.
"The one that stands out is the FA Cup semi-final, but even before that we've got big games and we've got to go to Man United as well so there's a chance to play this season."
Arsenal sit second in the table after winning 10 of their last 11 league games, while they face Reading at Wembley in the last four of the FA Cup on April 18.
