The England international forward ruptured his anterior cruciate ligament during an FA Cup game against Tottenham early in 2014 and missed out on the Three Lions' World Cup campaign.
While the former Southampton man continues to recover, Wenger has suggested that new signing Alexis Sanchez will be deployed on the right, but he is happy with Walcott's efforts to regain fitness.
"He's progressing very well," the Gunners boss told the club's official website. "He's worked very hard during the summer and we expect him to be back in full training at the end of August.
"[When he'll be back on the pitch is] difficult to predict. Once he's back in full training it can be very quick. He has a good basis, which is what he's working on now."
Since joining the north Londoners from Southampton in January 2006, Walcott has made nearly 200 Premier League appearances for the club, with an overall goal record of 69 from 281 matches in all competitions.