The 22-year-old has not featured since fracturing his foot in a friendly against Denmark in March but Arsenal manager Arsene Wenger said on Thursday that he was in line to play against Norwich.
Midfielder Aaron Ramsey and defender Kieran Gibbs may also be in the squad but utility player Alex Oxlade-Chamberlain remains sidelined.
"Ramsey could be available and Wilshere too," Wenger told a news conference. "Gibbs is also back in the squad, he has been doing normal training, but Oxlade-Chamberlain is still out."
England manager Roy Hodgson will announce his squad for next month's World Cup in Brazil on Monday and Wilshere, capped 15 times, is likely to be named if fit.
Arsenal meet Hull City in the FA Cup final at Wembley six days later.
Victory would end a nine-year wait for silverware for the Londoners but having secured a top-four finish and Champions League football for the 17th successive time, Wenger said they needed to improve in attack next season.
Arsenal were top of the Premier League for 128 days this term but faded in recent months and leaders Manchester City now hold a two-point advantage over Liverpool heading into the final day of the season.
"It was a season where City just won it, getting over the line," said Wenger. "They won the marathon and they turned up in the last 100 yards.
"It was not easy for them. Liverpool had an outstanding second part of the season. They are maybe the most unlucky team of the season. They were nearly there.
"We have been 128 days top of the league so we have won the stamina league. But we faded in big games away from home.
"City scored 100 goals. We have scored 66 at the moment. That's where we have room for improvement."
Wenger said France defender Laurent Koscielny was close to signing a new contract, having joined from Lorient in 2010, but he did not expect many incoming transfers until after the World Cup.
"In my experience, in a World Cup year, the transfer business does not get done early," he explained.
(Reporting by Josh Reich; editing by Tony Jimenez)
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