Old Trafford reportedly has an eye for Ramos and fellow defenders Raphael Varane and Raul Abiol, according to the Daily Star.
The speculation only adds to Ramos and Mourinho's alleged feud this season. The Spanish international publicly called out his coach after Real lost to Sevilla in La Liga play, and then found himself on the bench for the club’s subsequent Champions League match against Manchester City.
Recently, Mourinho started Ramos at full back in Madrid’s win over Deportivo La Coruna Sunday, and speculation intensified of a widening gap between player and coach.
"If I had to choose I would play centre back," Ramos said to ESPN. "But I am not here to get into debates with the coach, neither criticisms nor praise.
"Nobody can criticise my attitude. We are not machines or robots, and can have bad days. I live or die by my ideas - if I do not like something, why should I not say it? I will not stay quiet. Nobody can doubt my work or loyalty to this club."
It is unclear if Real Madrid would be interested in moving the 26-year-old, or if United could meet his estimated market value of £35 million.
The possible departure of Varane, who has made 10 appearances for Los Blancos since joining the club in 2010 from French Ligue 2’s Lens, would probably not hurt Real Madrid too much. Perhaphs the wealthiest club in the world, Real Madrid can likely find a suitable replacement for Varane.
Albiol, 27, has been a staple in Real Madrid’s defense, making 65 appearances since 2009.
Sitting at sixth in the La Liga standings, Real Madrid may consider a shake up to make a late-season surge. They have already lost two games during league play this season after six matches, compared to two losses after 19 games in 2011-12.
The possible addition of Mexican native Hernandez, who signed with United in 2010 from Guadalajara, may increase Los Blancos already potent attacking. The 24-year-old has netted 24 goals in 59 appearances with the Red Devils, but has played in only four Premier League matches this year, notching one goal and one assist.