Ozil's contract with Arsenal runs out at the end of this season, and he has been linked with a move to Premier League rivals United, where he could rekindle his relationship with Jose Mourinho after playing under him at Real Madrid.
And Wright is convinced that the former Real Madrid playmaker, who is also a target for Barcelona, will turn down a new deal with the Gunners and move to Old Trafford for free during the summer.
"Mesut Ozil on a free to Manchester United looks a shoo-in," Wright told the BBC. "I'm sure Jose would love to do that.
"That would frighten me to death. He is a great talent and having great players around him would lift him up as well.
"I'm sure him and his agent would not push it this far if they were going to sign (for Arsenal)."
The German international will be free to talk to any foreign clubs and sign pre-contract agreements from January 1st, but Mourinho is hoping his relationship with Ozil will help to convince him to snub interest from elsewhere, and move to Manchester instead.