The Austria international made the move to Bernabeu in July 2021 following the expiration of his contract at Bayern Munich, and he has made 85 appearances for the club, scoring five goals and registering seven assists.
The 31-year-old was again a vital player for Carlo Ancelotti's side during the 2022-23 campaign despite some fitness issues, featuring on 39 occasions in all competitions, although he only made 23 La Liga appearances, missing a chunk of action due to injury.
Alaba has a contract at Bernabeu until June 2026, placing Real Madrid in a strong position when it comes to his future, but there is currently speculation surrounding a possible summer exit.
According to El Nacional, Man United are 'very serious' about signing Alaba, with the English club's head coach Erik ten Hag 'obsessed' by the Austrian.
The report claims that an offer of €50m (£42.9m) would be seriously considered by Los Blancos, who are already believed to be looking at the market for potential replacements.
Alaba has already won six trophies during his time at Bernabeu, including La Liga, the Copa del Rey and the Champions League.
The defender won 10 Bundesliga titles during his time at Bayern, meanwhile, in addition to two Champions League trophies during a highly-successful spell.
Real Madrid currently have three players battling for the two starting roles in central defence, with Antonio Rudiger and Eder Militao also present at the club.
Man United, meanwhile, have Raphael Varane and Lisandro Martinez as their first-choice centre-backs, with the pair back to full fitness following injuries in the second half of last season.
Varane and Martinez are set to start the campaign at the back, while Victor Lindelof finished last season well and is set to stay at Old Trafford this summer despite some speculation surrounding his future.
Red Devils head coach Ten Hag has also said that he wants to keep Harry Maguire this summer despite the ongoing speculation surrounding a potential departure.
Maguire only started eight Premier League games last season, though, and is expected to again find it difficult to secure regular action if he stays this summer, which could lead to his departure.
Axel Tuanzebe and Phil Jones have also left this summer, while Eric Bailly is not in Ten Hag's plans for the new season and is set to leave, potentially becoming the latest high-profile player to make the switch to Saudi Arabia.