Standard Sport understands the Blues gave City the greenlight to sign the 29-year-old this summer with incoming manager Mauricio Pochettino allowing him to depart.
Pep Guardiola could lose influential midfielder Ilkay Gundogan this summer amid interest from Arsenal, Barcelona and clubs in Saudi Arabia.
Bayern Munich and former Chelsea manager Thomas Tuchel have also been credited with an interest in Kovacic, who has made 221 appearances for the Blues since joining in 2018.
Speaking to Nacional while away on international duty, Kovacic said: “I have one more year with Chelsea, this season was very bad.
“Everything is going towards the fact that after 5 good years I will change, but in football anything can happen. Right now, I’m focused on Croatia and the Nations League.
“Manchester City is a top team and deserves to be in the Champions League final. That’s what I have to say. The summer is long, we’ll see what happens.
“Chelsea is phenomenal for me. I love the city and the fans, they love me, I have wonderful memories of Chelsea. We’ll see what happens”
Chelsea are targeting a move for Brighton midfielder Moises Caicedo after cooling interest in Sporting Lisbon star Manuel Ugarte, who now looks set to join Paris Saint-Germain.
Mason Mount has agreed terms with Manchester United and N’Golo Kante is edging closer to a move to Saudi Pro League side Al Ittihad as part of a major midfield rebuild under Pochettino.
