United remain keen to strengthen their defence before the deadline passes at 5pm on August 8, having conceded the second-most goals of sides in the Premier League’s top 10 last time.
However, the Norwegian also wants to bring in another centre-back to play alongside Swedish star Victor Lindelof over the course of next season.
The Old Trafford side reportedly have placed Umtiti on their shortlist of targets, along with Leicester centre-back Harry Maguire.
But with the window for British clubs closing next Thursday, the Red Devils are running out of time to wrap up a move for either player.
Spanish publication Sport report that even though Barcelona are open to the idea of the France international leaving this summer, they are yet to receive a firm offer for the World Cup winner.
Barca will not entertain any offers of less than €60m for the former Lyon centre-back, who has a release clause of €500m written into his contract.
With time ticking down in the transfer window, it looks unlikely Umtiti will now depart the Camp Nou this summer and the player himself has previously expressed a desire to stay with the La Liga heavyweights.
United, meanwhile, are still targeting Maguire as their first-choice centre-back, but face a race against time to get the deal done.
Despite a rumoured asking price of £90m, which would be a world-record fee for a defender, the Red Devils remain keen on bringing the England international to Old Trafford before the window shuts next week.