The Spain international has 11 months left to run on his contract.
A recent report suggested that the Red Devils had made contact with the Spaniard’s representatives to discuss a potential move in the ongoing transfer window.
According to Italian journalist Fabrizio Romano, Los Blancos are set to join the race for Ruiz’s signature, and could sign him as a free agent in summer 2023.
While Manchester United are lining up a move this summer, Real Madrid are prepared to wait until the 26-year-old playmaker becomes a free agent next year.
The La Liga champions will explore the possibility of a free transfer next summer.