Bradford believe they may be owed a cut of Cleverley's loan fees as he was on their books before moving to United as a youngster.
The club's joint-chairman Mark Lawn told The Sun: "We're currently in discussions with United.
"They are a professional and sensible club so I don't see a problem.
"We're saying that this is the contract and we believe we're owed money so we're waiting for them to get back to us."
Bradford reportedly believe they are entitled to 10 per cent of all loan fees plus interest that has built up over the time the fees have not been paid.
They would also be entitled to a cut of any future transfer fee from United.
Cleverley has spent time on loan at Leicester City in League One and Watford in the Championship after spending last season at Wigan Athletic.
The player has picked up a league winners' medal with Leicester and was voted as Watford's player of the year.
Cleverley broke into United's first team this summer and could have been in line for a senior England debut before Wednesday's friendly with the Netherlands was called off.