Barca have been pushing Umtiti to discuss new terms in order to raise his current €60m buyout clause.
Sport says United spoke to Umtiti over the January transfer window.
And while a move to Old Trafford never materialised, the contact with Jose Mourinho has turned Umtiti's head.
Umtiti and Barcelona have agreed that the player will sign a new contract next year. His current deal expires in 2021.
United were willing to offer Umtiti a £5.3m yearly wage AFTER tax and Umtiti wants Barcelona to match that offer or he will consider his future at the Nou Camp.