The 26-year-old could leave Liverpool as early as January, with Real seeking a replacement for Dani Carvajal, who suffered an anterior cruciate ligament injury. Alexander-Arnold will be free to talk to foreign clubs in January.
However, Alexander-Arnold isn't the only right-back option that Liverpool are monitoring.
Carlo Ancelotti's side are said to be tracking a highly-regarded international who plays in the Bundesliga.
Real Madrid are reportedly considering an alternative signing to Trent Alexander-Arnold
Real Madrid are assessing Bayer Leverkusen's Jeremie Frimpong, according to ESPN.
Frimpong, who usually operates as a right wing-back, could join Real after Dani Carvajal suffered an anterior cruciate ligament injury.
A youth team player at Manchester City, Frimpong made his first steps into senior football with Celtic before signing for Leverkusen in 2021.
He has eight senior caps for the Netherlands, having made his international debut in 2023.
Real Madrid are currently in second place in LaLiga, three points adrift of leaders Barcelona.
The experienced Lucas Vazquez is capable of playing at right-back, but Real are in need of a longer-term option.