The England international has been linked with the European champions for some time, and the Spanish giants could snap him up on a free at the end of his contract next summer.
As reported by the Independent, Real Madrid are prepared to assert their financial power next summer after their blockbuster free signing of Kylian Mbappe over the recent transfer window.
It's claimed that Real Madrid also plan to sign Rodri, after his heroics for both Manchester City in recent seasons, and Spain who he helped lead to Euro 2024 glory.
Real Madrid then plan to sign one of the two other Premier League stars on their shortlist, those being Arsenal defender William Saliba, or his Tottenham counterpart Cristian Romero.
Real Madrid also want to buy one of Arsenal's William Saliba (left) or Tottenham's Cristian Romero (right)
Alexander-Arnold's contract situation arguably makes him the most obtainable out of the four players linked to Real Madrid.
However, the Reds are determined to keep him on their books and it could take some persuasion by Los Blancos to tempt the 25-year-old to leave his boyhood club.
A move to the Santiago Bernabeu though would see him link up with close friend Jude Bellingham.
It would take an incredible sum of money to sign Rodri from Manchester City, especially given the Spanish midfielder is contracted with the Premier League champions until 2027.
Their midfield lynchpin has become a strong contender for the Ballon d'Or given his success for both club and country.
The Athletic meanwhile have reported that City are trying to get the 28-year-old to sign a new contract extension as quick as possible.
Any new deal would put him close to Kevin De Bruyne and Erling Haaland as the club's top earners.
Real Madrid are already stacked in midfield with the likes of Bellingham, Aurelien Tchouameni, Eduardo Camavinga, Luka Modric and Federico Valverde already on their books.
Premier League defenders Saliba and Romero are also tied up with Arsenal and Tottenham respectively until 2027.
Saliba has played a huge part in Arsenal's challenge for the Premier League title in recent seasons, while World Cup winner Romero has been a regular in the Tottenham starting line-up and is a secondary option to the Gunners star.
Reports from Spain suggested that Real Madrid sent a scout to Sunday's north London derby, which saw Saliba's Arsenal side pick up a 1-0 victory over Romero's Tottenham.
Romero was beaten in the air by Arsenal counterpart Gabriel for the deciding goal of the match.