Manchester United have been given permission to approach Raphael Varane and are negotiating personal terms ahead of a potential move from Real Madrid.
If terms can be agreed, United are expected to open talks with Real Madrid over a fee - although Paris Saint-Germain are also in talks with Varane's camp.
It is thought the 28-year-old centre-back would be open to the move if an agreement can be reached.
- Man Utd interested in Eduardo Camavinga signing
- Man Utd confirm agreement to sign Jadon Sancho
- Premier League summer transfers: Club by club
United are believed to be cautious as they do not want a repeat of what happened with Sergio Ramos in 2015, when they were given encouragement the player would come to Old Trafford - only for him to sign a new contract at the Bernabeu.
Varane still has a year left on his Real Madrid contract and United are keen to negotiate a lower transfer fee knowing he is free to sign a pre-contract agreement in January.
The France international is one of a number of centre-backs United are looking at this summer as they make the position a priority to strengthen.
The Premier League side have also moved to strengthen their attack, completing a deal to sign England international Jadon Sancho from Borussia Dortmund for £73m, subject to a medical.
Varane would be another significant statement of intent to compete with Manchester City for the Premier League title next season, having established himself as one of the world's best defenders since joining Real from French side Lens in the summer of 2011.
He has gone on to make over 350 appearances for the club, and be capped 79 times by France, helping them to World Cup glory in 2018 and starting all four of their matches at Euro 2020 before they were knocked out Switzerland.
Varane: Missing piece in Man Utd's defensive puzzle?
Sky Sports' Jack Wilkinson:
Let's face it, despite undoubtedly improving as a defensive pair throughout last season, Harry Maguire and Victor Lindelof are yet to give off the air of confidence and authority to suggest they will be the centre-back pairing that sends Manchester United back into title contention.
Rightly or wrongly, Lindelof has always been viewed as the weak link in the partnership, while Eric Bailly has been out of the conversation completely. Sourcing an upgrade to sit alongside Maguire has been earmarked as an area of improvement for United and in Raphael Varane, they may just have found what they're looking for.
Few defenders in world football have the pedigree or resume to match that of the 28-year-old World Cup-winning Frenchman, who would arrive at Old Trafford with four Champions League winners' medals and three La Liga titles after a trophy-laden decade at Real Madrid.
A handful of shaky performances in France's run to the last-16 at Euro 2020, coupled with Real's apparent willingness to part company with a player in the peak years of his career, should raise cautionary red flags for United.
But the prospect of establishing a back four of Varane and Maguire at centre-back, with Luke Shaw and Aaron Wan-Bissaka in the full-back positions, would undoubtedly represent a step up in quality.
Maguire has proven for club and country he has the leadership qualities and technical ability to shoulder expectation, with the pace and experience of Varane in tow, United would have their strongest defensive line-up since they last won the title.