The England midfielder’s 20-minute cameo at Hull on Monday was his first appearance since November, when a foul from Manchester United’s Paddy McNair left him needing ankle surgery.
A 3-1 win on Humberside was Arsenal’s eighth in nine league games, and maximum points from their remaining four matches would guarantee the runners-up spot.
Arsene Wenger’s side last achieved that 10 years ago and, although they are still nine points short of last season’s tally of 79, Wilshere believes genuine improvements have been made.
“(Finishing second) would set a marker for next season and would be a progression from last year,” he told the club website.
“The last few seasons we’ve finished fourth so to finish two places ahead of that would be a massive progression for us and hopefully will give us confidence going into next season.”
Arsenal’s form means Wilshere has been forced to watch from the bench in recent weeks, but the target now is to get more time on the pitch between now and the summer.
He said: “It’s frustrating when you’re out but when you’re back on the pitch it makes up for all the time you spent injured.
“It’s much better for me to come into a team who are winning and playing as well as that. It’s easy because you can fit in when the boss is ready to include you.
“I’m just happy to get back on the pitch and get some minutes under my belt. I feel fitter for it, I’ll train next week and hopefully get some minutes next week as well.”