Mendy, a France international, is linked with a €50million move to the LaLiga giant after two seasons with Lyon.
However, the Ligue 1 outfit dismissed reports it has already reached an agreement with Madrid for the left-back.
"Olympique Lyonnais denies an agreement with Real Madrid for the transfer of international defender Ferland Mendy, contrary to what has been reported by some media outlets," the club wrote on Twitter.
Zinedine Zidane has already started a rebuild at Madrid after a poor 2018-2019 season in which they finished third in LaLiga and 19 points behind champion and rival Barcelona.
Real Madrid signed striker Luka Jovic from Eintracht Frankfurt on and is expected to bring in Chelsea star Eden Hazard.