The England international has emerged as a key man at Wanda Metropolitano, making 28 starts as Atletico won this season's La Liga title.
However, with just 12 months remaining on his contract, the 30-year-old is said to be keen for a return to the Premier League.
According to Football Insider, United have already had a bid of £10m rejected by Atletico as they bid to recoup closer to the £20m which they paid two years ago.
Aware that Old Trafford is his first-choice destination, United are expected to increase their offer over the coming weeks.
Atletico may be open to a sale if they can secure a like-for-like replacement over the summer. body check tags ::