Madrid have identified the German international along with Tottenham striker Harry Kane as a potential transfer target to replace Karim Benzema.
Havertz has two years left to run on his contract at Stamford Bridge and Chelsea are willing to entertain offers for the 23-year-old this summer, as new head coach Mauricio Pochettino targets a new forward to lead his attack next season.
But Chelsea want to recoup the £75.8m they paid to sign Havertz from Bundesliga side Bayer Leverkusen in the summer of 2020.
The 23-year-old is thought to be keen on a move to Madrid, who are also interested in Inter Milan forward Lautaro Martinez.
Ballon d’Or holder Benzema has announced he is leaving Real Madrid this summer after 14 years and a glut of major silverware and is expected to sign for Saudi Arabian side Al-Ittihad on a lucrative two-year contract.
Havertz has made 139 appearances across all competitions in three seasons at Chelsea, scoring 32 goals including most memorably the winner against Manchester City in the 2021 Champions League final in Porto.