Chelsea are willing to listen to offers for Ramires and could be prepared to sell him in January.
Jose Mourinho has told Stamford Bridge chiefs that he would be prepared for the Brazilian to leave if a proven midfield replacement can be found.
Spanish clubs, led by Real Madrid, are understood to be monitoring Ramires' situation closely.
The 27-year-old has struggled with injury and poor form this season, starting just three of the team's 16 matches in all competitions.
He has been overlooked in favour of Premier League ever-presents Nemanja Matic and Cesc Fabregas for the central midfield slots and has had to fight with the likes of Eden Hazard, Oscar, Willian and Andre Schurrle for an attacking midfield position.
Since returning to Stamford Bridge last season for his second spell at the helm, Mourinho has been ruthless in discarding high-profile players whom he does not regard as automatic starters.
Juan Mata, David Luiz and Romelu Lukaku are among the big names to have been sold on for considerable profit, while the likes of Fernando Torres, Demba Ba, Frank Lampard, Ashley Cole and Kevin De Bruyne have also been shown the exit door.
Speaking about Ramires last week, Mourinho said that he was pleased to have the Brazilian available again.
"Ramires is very important to us," the manager observed. "He is good tactically and can play in multiple positions with the same intensity.
"He's a dangerous guy when attacking and has a good defensive transition. He has a fantastic engine when pressing and that is important to us. The balance between the technical players like Ramires and the athletes is important."