The Turkish giants were previously linked to United and Brazil midfielder Casemiro.
A possible double swoop may be on the cards, with Fanatik stating that Varane is on their radar.
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The Frenchman is out of contract and can leave as a free agent if the club does not get him to sign a new deal.
United are thought to be content to let Varane leave, given his various injury problems.
The Frenchman has failed to sustain a run of 10 to 15 starts in a row since arriving from Real Madrid.