Kovacic, 24, expressed his desire to leave Real Madrid in search of first-team football during the World Cup.The midfielder was limited to just 10 La Liga appearances last season.
Kovacic completed a move from Inter Milan to Madrid back in 2015 but a lack of game-time at the Bernabeu means the 24-year-old is keen for a move ahead of the 2018/19 campaign.
He was part of Croatia’s squad but played just 183 minutes of their run to the final.
Chelsea were offered Kovacic on a season-long loan, plus £35m, as part of a swap-deal for Thibaut Courtois.
Goalkeeper Courtois is expected to arrive at Real Madrid on Thursday ahead of completing a move to the Santiago Bernabeu.