Ramos, 26, who was dropped for Real's Champions League clash against Manchester City, had a bust up with boss Jose Mourinho. A few weeks ago Real forward Cristiano Ronaldo claimed to be 'unhappy' with the club.
However, according to reports in Madrid, if Ramos and Mourinho fail to maintain a good relationship, Madrid may have to sell the 26-year-old.
Chelsea are now clear favourites to land the Spaniard after failing to sign Inter Milan right-back Maicon, who joined Manchester City.
Chelsea boss Roberto Di Matteo is keen on strengthening his back line with an experienced defender as Ramos can play both in the centre as well as in a full-back position.
Ramos, who has 366 caps with Madrid, joined Los Blancos in 2005 for a record 27 million Euros from Sevilla. The 26-year-old already has 95 caps with the national side and has taken part in three major tournament finals so far.