Hernandez played a key role in France winning the 2018 World Cup, and only signed a new long-term contract with Atletico this summer.
However, according to France Football, United have not been put off by Hernandez's release clause of £72m, and could move for the 22-year-old at the end of the season.
United boss Jose Mourinho was unable to bring a new central defender to the club during the summer transfer window, despite the reported interest in Leicester City's Harry Maguire and Tottenham Hotspur's Toby Alderweireld.
Hernandez operated at left-back for France during the 2018 World Cup but can also play in central defence.
The Frenchman is fast closing on 100 first-team appearances for Atletico.