The 20-year-old midfielder missed the whole of last season with ankle and knee problems and the Gunners are yet to set a date on a return this term, although he is unlikely to feature before October.
Wenger admits his lengthy spell on the sidelines “has not been easy to take” for the England midfielder and the Arsenal boss is hopeful his move to give him the north London club’s prestigious No10 shirt will help to keep him motivated as he works towards a return to action.
“I feel Jack will be one of the leaders of this club and by giving him the No10 shirt I want to show I am confident he will be the one who will lead the team one day,” said Wenger.
“I believe that he is at the stage where he needs something at the moment. At his age after one year out, that is not easy to take.
“Every day he comes in at eight o’clock in the morning and works out but didn’t get anywhere. I want to show him that I believe in him and that he will come back quickly.”
Wenger, who saw Van Persie unveiled as a Manchester United player on Friday after the Gunners reluctantly sold their captain in a £24m deal, is keen not to dwell on the striker’s departure, preferring to look forward at his team’s “fantastic potential”.
“We lose great players but I want to show that we have great players at the club,” he added. “We have young players, English players like [Alex] Oxlade-Chamberlain and Wilshere. We have fantastic potential here and when everyone is fit we will see that.”