The Spaniard is reportedly unhappy at the Bernabeu and the Blues are keen to add a defender to their squad.
The Blues are reportedly looking to sign another central defender during the summer transfer window as Jose Mourinho aims to boost his title winning side.
Currently they have veteran John Terry and Gary Cahill as the first choice centre-back pairing, but the former England captain is not getting any younger and would do well to play every single game as he did last season.
Outside of those two, they currently have French youngster Kurt Zouma as back up and despite him impressing when called upon last season, he is not yet ready to be a first choice centre-back in the Premier League.
That has led to the Blues being linked with several defenders so far, with Ramos now joining the list. The Spaniard is rumoured to be unhappy at the Bernabeu after the surprise appointment of Rafa Benitez.
He is also yet to agree a new deal at the club, with his current agreement set to expire in 2017, and the report claims he has asked for as much as £10 million-per-year to stay with the La Liga giants.
If he were to leave, it is likely that Chelsea would face stern competition for his signature, with Premier League rivals Arsenal and Manchester United both being credited with an interest also.