The Cottagers insist United have broken Football Association rules governing the pricing of tickets for Cup matches, says the London Evening Standard.
And the FA have responded to Fulham's official complaint by ordering United to explain why they have offered their fans an exclusive £5 discount.
The clubs agreed travelling fans and United supporters in similar seating would pay £45 for the game but the Old Trafford club have since offered the discount to members, season-ticket holders and multiple-ticket purchasers.
A Fulham spokeswoman said: "We are not happy about penalising our fans and that is essentially why we made the complaint to the Football Association.
"The rules state that you must agree with the opposition club if you intend to discount any of your tickets and that is what Manchester United haven't done. So they have effectively broken an FA Rule.
"They have to have agreed it with us first, they didn't do that, and we are now having to penalise our fans paying for a full-price ticket whereas their fans will get a discount. We would never have agreed to that."