According to Spanish outlet Diario Gol (h/t James Benson of the Daily Express), Gerard Pique has informed Messi the defender could move to Old Trafford if the Camp Nou giants do not offer him an improved deal. Umtiti wants his club to double his wage, with United ready to step in if fresh terms cannot be agreed.
Umtiti has reportedly said he will leave for the Premier League if his demands are not met by the La Liga leaders.
Kris Voakes and Ignasi Oliva of Goal had reported the France international was close to agreeing an extended stay with Barca, but the latest news suggests Umtiti's future remains undecided. Barca are keen to retain the centre-back but must negotiate around Financial Fair Play rules after signing Philippe Coutinho for €160 million (£142 million).
United have been solid in the Premier League this season, but they still need to add a top-level centre-back if they hope to compete for the title.
Eric Bailly's absence has robbed manager Jose Mourinho of one of his first-choice defenders, and the Red Devils lack a reliable partnership at the heart of their back four.
In other United news, the Old Trafford giants are focused on raiding Barca for Ivan Rakitic.
Per Diario Gol (h/t Beya Kabelu of The Sun) reported the 29-year-old is seeking "clarification" from the club about his future at the Camp Nou.
United have found it difficult to find an effective partner for Paul Pogba in midfield, with Mourinho switching back and forth between 4-3-3 and 4-2-3-1 formations.
Pogba has been forced to play a more defensive role, but it is clear he is happier on the front foot.
Rakitic's technical ability would help United control games in midfield, and with Michael Carrick set to retire at the end of the season, the Red Devils will need an addition in the engine room.
Despite significant spending, Mourinho looks set to splash the cash once again in the summer to fill key holes in his team.