The 27-year-old informed Spurs of his desire to seek pastures new earlier this year, and Man City have long been regarded as the favourites to secure his signature in the current market.
According to The Sun, Levy is prepared to sell the England captain to the Premier League champions for £160m, with the forward set to pen a deal in Manchester worth £400,000 a week.
The report claims that the Tottenham chairman told Kane and his agent at the end of last week that he was willing to give the green light on a switch to the Etihad Stadium.
The striker enjoyed an excellent 2020-21 campaign at the Tottenham Hotspur Stadium, scoring 33 goals and registering 17 assists in 49 appearances in all competitions.
Kane also played a key role for England at Euro 2020, scoring four times in seven appearances, as the Three Lions made the final of the competition before losing to Italy.