The Citizens were strongly linked with the England captain over the summer, and the club's head coach Pep Guardiola openly admitted that the Premier League champions were trying to sign the striker.
Man City ultimately could not agree a transfer fee with Spurs, though, with the North London club thought to have placed a £160m asking price on the 28-year-old.
According to Eurosport, Guardiola's side are unlikely to pursue Kane next summer despite the club being keen to improve their attacking options moving forward.
A recent report claimed that the Englishman is open to signing a new deal at the Tottenham Hotspur Stadium, providing that a release clause is included in the agreement.
Kane, who has three years left to run on his current deal at Tottenham, has scored twice in four appearances at club level this term but is yet to register in three Premier League outings. body check tags ::