Spurs boss Jose Mourinho was keen to take the England star on a season-long deal and offer him the chance to revive his flagging career.
But it is understood the centre back is reluctant to uproot his family and move to London, despite falling down the pecking order at the Etihad.
Stones has made just one appearance for Pep Guardiola's side this season, but will not commit to leaving the Etihad until the Spaniard tells him he is no longer wanted.
Tottenham boss Mourinho is desperate to bolster his back-line in the final few hours of the transfer window.
Inter Milan star Milan Skriniar has been linked with a move to north London as has Chelsea ace Antonio Rudiger.
And Tottenham’s focus may have to go back to that duo with Stones not joining despite Guardiola strengthening his own defence this summer.
Nathan Ake and Ruben Dias have joined City this summer and both are ahead of Stones when it comes to a place in Guardiola’s squad.
Guardiola had said earlier this summer: “I’ve said many times, and continue saying, I’m more than delighted with John Stones as a person, as a professional, everything.
“What I want is the best for him and at the end of the season we are going to speak about what is going to happen, because sometimes my wish is not the wish of the players, or the wish for the situation of the club.
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“I am honest with them and the moment I will feel – not with John but any player – if we have to change we are going to tell them.”
Stones joined City from Everton in 2016 with the Etihad outfit paying £47.5m for the former Barnsley gem.
Though he has never made more than 27 Premier League appearances for City in one season, featuring in less than half the games last campaign.