The club have confirmed that the complaint was lodged to football's governing body today.
"On 27th May, Manchester United made clear its intention to report Real Madrid to FIFA if it continued to involve itself in the future of Cristiano Ronaldo," read a club statement.
"Unfortunately, Real Madrid has not kept its own counsel and the club feels it has no alternative but to make a formal complaint to the world governing body, which it has done today.
"The precise content and nature will remain confidential."