The 24-year-old's current deal with River is due to expire in December 2022, and it is believed that the Uruguay international is keen to seek pastures new.
According to Fichajes, Man United are interested in the attacker, but the Red Devils will have to hold off competition from La Liga duo Sevilla and Atletico in order to sign him.
De La Cruz, who is capable of operating in a number of different midfield positions, has scored 23 goals and registered 29 assists in 130 appearances for his current side in all competitions.
Earlier this year, it was claimed that Man United forward Edinson Cavani had urged his club to make a move for the player that he operates alongside at international level.
De La Cruz could allegedly be available for as little as €16m (£13.7m) due to his contract situation.