The Ukrainian goalkeeper's contract is set to expire in less than a year.
Transfer expert Ekrem Konur is reporting: "Andriy Lunin has made a significant decision regarding his future at Real Madrid.
"With his contract set to expire in 2025, Lunin is not keen on staying at Real Madrid and is considering a move to another club."
Lunin is strictly second choice at Real behind senior No1 Thibaut Courtois.