The 31-year-old confirmed on Tuesday that he will be leaving the Red Devils when his contract expires at the end of the season.
Varane has spent the last three seasons as a Man United player, playing 93 times in all competitions, and he is set to make his final appearance at Old Trafford on Wednesday against Newcastle United in the Premier League.
The Frenchman has thanked the supporters and all those associated with Man United for making him welcome on the red side of Manchester, and he has also heaped praise on the "clear plan and great strategy" set out by new minority shareholder Sir Jim Ratcliffe.
Significant changes have already been made at boardroom level since the arrival of Ratcliffe, and his focus will soon shift to the summer transfer window when player incomings and outgoings are to be expected at Old Trafford.
Branthwaite, Bremer, Tapsoba on Man Utd's radar
According to the Manchester Evening News, Man United will prioritise additions in central defence and could look to recruit at least two centre-backs ahead of the 2024-25 season.
While Varane has now confirmed his exit, Jonny Evans is out of contract at the end of June, and Victor Lindelof is believed to be facing an uncertain future at the club.
Lisandro Martinez and Harry Maguire are the only other senior centre-back options at Man United, who have struggled defensively all season, conceding a total of 82 goals in all competitions for the first time since 1970-71.
With all that in mind, Man United are said to have identified Everton's Jarrad Branthwaite, Juventus' Gleison Bremer and Bayer Leverkusen's Edmond Tapsoba as three potential targets ahead of this summer's transfer window.
Branthwaite has been heavily linked with Man United ever since he established himself as a first-team regular at Everton earlier this season.
The 21-year-old has helped the Toffees keep 12 clean sheets in 34 Premier League appearances this term, and because of his fine form at club level, he is in contention to earn an England call-up for Euro 2024.
Branthwaite is under contract at Goodison Park until June 2027, but it is thought that the youngster could be sold by Everton this summer amid their financial concerns.
Meanwhile, Brazil international Bremer has also been linked with Man United, with a recent report claiming that the Red Devils are weighing up whether to pay the £51.5m release clause in his Juventus contract.
As for Tapsoba, he has been an integral first-team defender for a Leverkusen outfit who have not lost any of their 50 games across all competitions this season and are on course to win a historic treble.