Kane, 27, has publicly expressed his desire to add trophies to his excellent goalscoring record and is believed to be keen on a move away from his boyhood club this summer.
Sky Sports reported that Spurs are expected to reject the bid with Tottenham chairman Daniel Levy holding out for at least £120m (€140m) for his prized asset.
Despite Kane winning the Golden Boot for top goalscorer and top assist provider last season, Spurs finished seventh in the Premier League and missed the Champions League for the second consecutive season.
By contrast, City claimed a third Premier League title in four seasons, but missed out on the club’s first ever Champions League by losing 1-0 in the final to Chelsea.
The English champions are looking for a replacement for all-time top goalscorer Sergio Aguero, who has left City after 10 years to join Barcelona.
Kane is yet to win any major trophy for club or country.
He is hoping to change that next month at Euro 2020, but his tournament has got off to a slow start.
Gareth Southgate has substituted his skipper in both matches, against Croatia and Scotland, and Kane has failed to score.
However, Southgate has already confirmed Kane will start Tuesday’s final Group D match against the Czech Republic.
I know there will be a lot of questions being asked about him at the moment but he has been through that 100 times before,” Southgate said on Sunday.
“I have answered that several times in the past and he has come up with the goals that have won us the next games and I expect that to be the same moving forward.”