However, there is an acceptance at the Etihad Stadium it will be a hard deal to get over the line with Tottenham chairman Daniel Levy valuing the England captain at more than £150 million. Kane also has three years left on his contract after signing a long-term extension in December 2016.
Manager Pep Guardiola and director of football Txiki Begiristain are keen to sign a striker following the departure of Sergio Aguero but there is also confidence that the squad would be able to cope if a new goalscorer does not arrive.
City wanted a central midfielder in the summer of 2018 and a centre-back in 2019 but in both instances waited 12 months before filling the gap in the squad. Midfielder Rodri arrived from Atletico Madrid in 2019 and defender Ruben Dias was signed from Benfica in 2020.
Sources have told ESPN that if Kane does not move to City this summer, they would be likely to revive their interest next year when Tottenham would be under more pressure to cash in. Erling Haaland would be another option if the Norway striker decides to leave Borussia Dortmund ahead of the 2022-23 season.
Sources close to Kane insist the 27-year-old remains fully focused on England's Euro 2020 campaign and does not expect any significant developments until after the tournament.
Tottenham remain in limbo just weeks away from the start of preseason training after failing to appoint a new manager in place of Jose Mourinho, who was sacked in April.