QPR and Norwich City are both interested in luring the Frenchman over to England before the end of the transfer window.
Varane, 22, is under contract at Sporting Gijon until the summer of 2027 and has made 15 appearances for them in all competitions during the first-half of this season.
L’Equipe claim the Hoops and the Canaries are keen on landing him but face competition from Cadiz and Getafe.
Varane started his career at Lens and rose up through the academy ranks of the Ligue 1 outfit. He was a regular at various youth levels before going on to play once for their first-team.
The Lille-born man was loaned out to Rodez to get some experience under his belt before leaving on a permanent basis as a youngster to join Sporting Gijon in 2022.
He was a key player for Sporting’s B team during his first 12 months in Spain and has now established himself a key player for their senior team.
His current club will face a battle to keep hold of him now amid interest from elsewhere.
QPR are fighting for their lives in the Championship and need reinforcements before the end of the month to boost their survival hopes.
Varane would give the R’s more competition and depth in the middle of the park and another option to pick from as they look to get some more points on the board under Marti Cifuentes.
However, promotion hopefuls Norwich are also in the frame. The Canaries are sat in 8th place in the table after their win over West Brom last time out and they are only two points off the play-offs.