The 27-year-old’s season has been hampered by injury, while his last eight appearances for the Gunners have been from the bench due to his inconsistent form.
Walcott is now a doubt to make Roy Hodgson’s squad, which will be named on Monday, but Wenger is backing his player to deliver at this summer’s tournament.
"I think he should go. He has gone through a bad spell. He has had a difficult period but in the last month, he has come back very strong," said the Arsenal boss.
"He could be a positive surprise for England."
Walcott has also been linked with a move away but with Danny Welbeck sidelined for nine months after requiring knee surgery, Wenger is keen to keep the forward: "He will be here next season."