The Telegraph says City are one of the few clubs who may be able to match Spurs' £150m price tag, but they are keen to thrash out a deal sooner rather then later, instead of waiting until the start of the season.
Premier League champions City are on the hunt for a new long-term successor to Sergio Aguero, who left the Etihad to join Barcelona on a free transfer. Kane was quickly earmarked as one of their targets.
However, City are not willing to battle away to secure Kane's signature right up until the end of the window.
There is nothing down in writing which would force Spurs chairman Daniel Levy to sell Kane this summer, despite contrasting rumours, and the club chief is determined to keep hold of him.