The Sun says Upamenco's £38m release clause is only activated in the summer.
Spanish reports claim the World Cup winner wants out of the Bernabeu, after winning 17 trophies since joining the club in 2011.
The 27-year-old's contract runs until the end of the 2021-22 season and Real would prefer to cash in on the defender rather than risk losing him for nothing.
However, United have scouted Upamecano, 22, for over a year and were close to agreeing a deal last summer.
But they stepped back when the player's father started making extra demands – opening the door for Liverpool to join the race.
United have continued to keep tabs on Upamecano, despite cooling on the deal in the summer, and will go head to head with Liverpool – if they do not move sooner.