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It is understood that City bid £100m, plus players, for Kane earlier this week before it was turned down by Spurs - who are believed to want at least £150m for their talisman.
As a result of his mammoth price tag, ESPN sources have claimed that the Citizens are likely to revive their interest next year when the north London club will be under more pressure to cash in.
Kane has three years left on his contract after signing a long-term extension in December 2016, but trophies have so far eluded him during his time at the club.
His future, however, is not expected to be decided until after Euro 2020, on which he is said to be fully focused at the moment.
In a disappointing start to the tournament, Kane - widely considered as one of the best strikers in the world - failed to score in England's first two matches and was substituted in both games.
ESPN's sources reiterated that there is an acceptance at the Etihad Stadium that it will be a challenge to get a deal over the line with Spurs - especially with chairman Daniel Levy valuing the striker at more than £150m.
Only time will tell if City has the patience with Spurs to get a deal over the line to sign Kane, but one thing is for sure, he wants to leave and win trophies - and at City, he can do just that.
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