Wenger splashed out in excess of £30m to sign Xhaka from Borussia Monchengladbach in May.
But Wright told The Sun Goals podcast that one of his mates thinks Wenger merely signed Xhaka to keep the fans happy.
"I can't understand it," the Arsenal legend said of Xhaka's lack of starts.
"Me and my mates were talking and one of my friends came up with the idea that Wenger's only bought him to appease people that he can spend a lot of money."
Xhaka, who captained Gladbach, has scored two screamers in consecutive games and Wright believes he is an Arsenal skipper in the making.
He added: "The sooner you can integrate Xhaka into the team, the way he plays, he will have an imprint on the team.
"He already has the capabilities to be a future captain of Arsenal."