Hernandez is able to play at left-back or centre-back and is seen by United boss Jose Mourinho as an ideal candidate to help solve his defensive problems at Old Trafford.
Mourinho is desperate to bolster his backline in January, having seen his side concede 14 Premier League goals already this season after failing to bring in reinforcements during the summer.
United chose not to splash the cash on the likes of Harry Maguire, Toby Alderweireld and Jerome Boateng during the previous window, but Spanish publication Marca reports that they have now made a 'dizzying offer' for Hernandez.
The World Cup winner has a £70m release clause in his contract at the Wanda Metropolitano, and United are understood to be willing to meet that as well as doubling his current wages.
The player is thought to be open to a move despite turning down Real Madrid in the summer, although Los Blancos still retain an interest while Manchester City are also rumoured to have already made an offer for the 22-year-old.
Hernandez joined Atletico in 2014 and has gone on to make 93 first-team appearances for the club.