Kane took extraordinary measures on Monday in his attempt to force through a deal to the reigning Premier League winners, refusing to report for pre-season training with Spurs.
The Citizens are thought to be the frontrunners to recruit the 28-year-old, who is seeking a move away from Tottenham in quest of silverware, but the north London club's high price tag appears to be deterring potential suitors.
City haven't given up hope of acquiring Kane, according to Daily Star Sport, although the two clubs' assessments of the England captain are still £40 million apart.
As a result of this, due to the deal's complexity, the discussions are likely to last several weeks. City will be gearing themselves for a race to the finish line before the transfer window closes on August 31.
City are said to have made a £100 million bid for the Aston Villa captain, despite his present club offering him a new deal in the hopes of keeping him in the Midlands.
City is expected to be extremely active in the coming weeks as they attempt to complete one of the largest transfer transactions in club history. Will they be able to get both Kane and Grealish? Keep an eye on this.
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