Chelsea are still looking to add pieces to their midfield this summer, despite appearing to be loaded in the department as they head into the upcoming campaign.
Jorginho followed Maurizio Sarri from Napoli earlier this month, while the Blues already boast the likes of Cesc Fabregas, N'Golo Kante, Danny Drinkwater, Ruben Loftus-Cheek, Ross Barkley and Tiemoue Bakayoko.
The Croatian has made his intentions clear this summer and is believed to be desperate to move on after failing to establish himself as a regular in Los Blancos setup. He has had several suitors up to this point, yet the Spanish giants are understood to have rejected every advance and aren't willing to sell.
According to Sportsmail, the Blues have identified the Madrid man as an alternative to Ramsey, who is currently in talks with Arsenal over a new deal, and have approached the Champions League holders with an enquiry.
Chelsea are said to be monitoring the situation with the Gunners star but may choose to wait until next summer, when they will be able to sign the Welshman for free, providing he cannot agree over new terms with Arsenal.
Sarri, meanwhile, is described as a huge admirer of Kovacic, having watched him closely back in his Inter days. But if there is indeed interest from the Chelsea camp, it's likely to be met with competition from Manchester City, who are still looking for a top-class midfielder after missing out on Jorginho.