England right-back Walker, who is weighing up his future at the Premier League champions, is also attracting interest from Saudi Arabia.
Walker has a year left on his City contract and has previously stated a desire to return to Bramall Lane, where he started his career.
The defender was snapped up by Tottenham in 2009 when the London club paid £9million for him and Kyle Naughton.
Walker was loaned back to Sheffield United for the 2009/10 season as part of the deal, but was recalled back to Tottenham in February 2010.
He then had further loans to QPR and Aston Villa before establishing himself as a Spurs regular in the 2011/12 season.
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Over the following six season, he wracked up over 200 appearances, and helping them finish in the top four in three of those campaigns.
City came calling in 2017 and agreed a deal of up to £50m for the star right-back.
Walker was 27 when he joined the Manchester club and had no trophies to his name, but quickly made up for lost time.
Since then, he has won 14 trophies and that includes five Premier Leagues and the Champions League.
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He has 254 appearances for City, but may have played his last game for the club.
The 33-year-old has one-year left on contract and saw his role in Pep Guardiola's side diminish in their treble winning campaign.