The Premier League champions are set to propose an upgraded offer for the England international this week, after Spurs declined an informal £100 million approach from the Manchester side for Kane in June.
City boss Pep Guardiola has admitted that his side are trying to negotiate a fee for the 28-year-old with Spurs chairman Daniel Levy, who has reportedly put a £150 million asking-price for the striker this summer.
Tottenham manager Nuno Espirito Santo has included Kane in his side's 25-man squad for their Europa Conference League play-off tie against Portugese outfit Pacos de Ferreira on Thursday, which reflects the club's desire to keep hold of their academy graduate past the ongoing window.
As reported by Sami Mokbel of The Daily Mail, City will walk away from a potential deal if Tottenham refuse to consider their improved offer for Kane this month, with several reports suggesting that the Etihad hierarchy are tabling a fee in the region of £120 million (plus add-ons) to sign the striker.
The Champions League finalists believe that they will be getting full value of a club-record sum if they manage to sign Kane, who turned 28 in July, before the end of the month, with the marksman's age and injury history becoming an increasingly crucial factor for City.
Moreover, it has been revealed that Kane's potential arrival to the Etihad Stadium has been openly discussed within the City dressing room, and his addition to a star-studded squad could prove to be a scary proposition for the rest of the league.
After failing to score in their opening two fixtures of the new campaign, both of which ended in defeats, City are ready to make a final approach to land Kane before the transfer window shuts on August 31.
Kane has informed Tottenham that he will be available to play and train for his current side, and that he has no intention of downing tools and forcing a move to the Etihad Stadium this summer.
It has also been mentioned that though Kane is intent on sealing a switch to City, the forward understands that a deal may not get over the line, with just two weeks left before the transfer window shuts.
It was reported recently that Kane is hoping that City will make an improved offer for his services this week, which would need to be in excess of the £100 million spent by the Champions League finalists to sign Jack Grealish from Aston Villa in early August.
Additionally, it has been stated that City had to get their league tie against Spurs out of the way before making a concrete attempt to land Kane,
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