Walker played only 2 minutes of Spurs' victory over Arsenal at White Hart Lane, coming on as a late substitute.
Having fallen out with Spurs boss Mauricio Pochettino once again over fitness and selection, and having been dropped several times recently with ex-City academy player Kieran Trippier getting the nod, Walker has decided it is time to look for his next club.
According to the Independent, who have presumably been briefed by somebody close to Walker, the "issue between Walker and Pochettino is long-running and boils down to Pochettino's doubts about Walker's fitness and his performances in training".
Is Pochettino preparing for life without Kyle Walker?
Manchester United, Manchester City and Barcelona are all said to be keen on signing him.
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Mauricio Pochettino benched Walker and included Trippier in the starting XI in his side's FA Cup semi-final defeat to Chelsea at Wembley.
Tottenham Hotspur defender Kyle Walker is linked with a move to Manchester City - but they gave away his replacement.
Bayern Munich also emerged as potential destination for Walker as it was reported a few weeks back that they have joined the race for his signature.
The England International will be well aware of the aforementioned clubs' ability to pay far greater wages than the reported £70,000 he now pockets every week and the prospect of challenging for the Champions League season after a season is an opportunity a seldom few let slip. This is despite signing a new contract at the start of the season.
The Independent believe Walker will set City back somewhere in the region of £35million-£50million, whilst Manchester Evening News claim Guardiola is already prepared for the fact he'll likely have to set a new world-record transfer fee for a full-back (perhaps even twice) this summer.