The Premier League new-boys see Gray, 19, as a potential successor for Jobe Bellingham. Bellingham is on the brink of signing with Borussia Dortmund.
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The Sun says defensive midfielder Gray has a year left on his City deal and could be cashed in if Sunderland firm up their interest.
Borussia Dortmund are expected to pay £25m for Bellingham, with part of that fee to go towards signing Gray.
Meanwhile, Chris Rigg is in talks with Sunderland over a new deal, this despite interest now arriving from Premier League rivals.