Gallagher moved to Atletico for £34 million in the summer of 2024 after being pushed out by Chelsea boss Enzo Maresca.
The England star has since thrived in La Liga, featuring in 69 matches and scoring six goals.
However, the 25-year-old expressed that he wants “more opportunities to be a starter” but said he was still "very happy" at the Spanish club.
Now, as per journalist Fabrizio Romano, United are keen on handing him those opportunities as they prepare a bid.
"I think there is a chance for Conor Gallagher to leave Atletico Madrid already in the January transfer window or eventually in the summer," Romano said.
"This will also depend on the formula of the deal. Manchester United were interested in Conor Gallagher as an opportunity in the final days of August, but Atletico said no to a loan move and they don’t have that kind of intention.
"I think if maybe a permanent transfer proposal arrives, that would be different. Maybe something around €30 million (£26m), sources say that this could be the way to get Conor Gallagher in the January transfer window."
It's become clear that United are considering adding new midfield options to their squad, as the Red Devils continue to be linked to the likes of Brighton’s Carlos Baleba and Crystal Palace’s Adam Wharton.
However, Gallagher may become the frontrunner to enter United’s midfield, which is set to lose Casemiro at the end of his deal in the summer.