"He will get stronger and stronger," Wenger told British media. "He has a basic fitness but needs a few games now. He needs two, three games more and he will be ready for England."
England face Russia, Slovakia and Wales in Group B of the 24-team tournament that starts on June 10 in France.
Wilshere, who has 28 caps for England, missed the whole of the 2011-12 season, including Euro 2012, with a stress fracture of the ankle.
Tottenham Hotspur's 5-1 defeat at Newcastle United on Sunday meant Arsenal finished in the top two of the Premier League for the first time since 2005, albeit 10 points adrift of champions Leicester City.
Wenger, who joined the north London club in 1996 and has led Arsenal to a top four finish in every full season, said there would be no lack of funds to buy new players for next season -- the last on his current contract.
"(Majority stakeholder) Stan Kroenke is completely behind myself and the board investing as much money as we want," he said.
"It has to be in respect of a balanced budget, we have resources but the problem is finding players.
"Everybody has money in England and they're all after good players."
(Reporting by Ian Rodricks in Bengaluru)
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