The Blues have already started their hunt to sign a new frontman before the start of the 2021-22 season and the 32-year-old forward is one of their primary targets.
Los Blancos boss Zinedine Zidane is thought to be eyeing attacking reinforcements ahead of a new season, as Karim Benzema turns 34 at the end of this year while Mariano Diaz has failed to establish his place as a first-team regular.
Chelsea have reportedly joined the race to sign Bayern Munich striker Robert Lewandowski.
The Blues are set for a major overhaul ahead of next season regardless of whether Antonio Conte stays or departs the Stamford Bridge.
The Polish international appears to be unhappy at the Allianz Arena and his agent Pini Zahavi is helping him try to find a new club, according to the Daily Star.
Bayern Munich star Robert Lewandowski has emerged as a major summer target for Real Madrid, according to his agent as per Marca.
The Spanish giants are keen on the Poland international at the end of the season, with reports suggesting that Real would ready to sell their talisman striker Cristiano Ronaldo to finance the deal.