The Gunners forward was prematurely sent home from the club’s training camp in Germany for inspection into the injury that had kept him sidelined.
However, the French manager revealed Walcott will be back in contention in a week and a half.
“He could, we are hopeful,” Wenger said to reporters ahead of the Emirates Cup this weekend.
“It is better than expected. He is ten days out.”
Asked if Walcott could make the start of the season clash against Newcastle on August 13, Wenger replied: “He could, we are hopeful.”