The German international eventually secured a reported £42.5m switch to Arsenal from Real Madrid on deadline day, but it has been claimed that a man posing as Ozil's representative tried to push through a move to Old Trafford.
The midfielder's father has produced a document, dated August 7, with what is alleged to be his forged signature.
"Someone wanted to make contact with Manchester [United] in my name and even signed with my name," Mustafa told German publication Express.
"That is no trivial offence. We will get to the bottom of it. I would have never deemed it possible what some dodgy people venture to do."
Ozil has helped the Gunners reach the top of the Premier League table since his arrival on September 2.