Jose Mourinho brought in several new defenders over the summer - as Marc Cucurella, Denzel Dumfries and Ibrahima Konate all landed in Madrid - but Mourinho is planning for life after Antonio Rudiger, who is set to leave when his contract expires in June 2027.
Mourinho wants double cover in each position, and that means another centre-back alongside Konate, Eder Militao and Dean Huijsen, with England international Quansah on his radar.
Los Blancos have sent scouts to watch the 23-year-old in action for Leverkusen and England in recent weeks and they are open to making a formal bid either in January or next summer.
Quansah is under contract in Germany until 2030, but the main block to a possible deal remains his link to Liverpool, who hold an option to re-sign him for €70M, up until July 2027.
The Reds have not indicated their stance over a reunion with Quansah, who they offloaded just over a year ago, and a call will likely depend on whether or not captain Virgil van Dijk agrees a 12-month extension.