Harry Kane spoke earlier at the end of last season about his desire to win tournaments more, as he reached his 28th year without winning any titles.
Manchester City are close to signing Aston Villa captain Jack Grealish in a deal worth up to 100 million pounds.
The Telegraph indicated that Harry Kane is now pressing his club, Tottenham, to join Manchester City, who is still aiming to sign the England captain, despite the expected great value of the Grealish deal.
Previous press reports revealed that Harry Kane may not return to Tottenham training after the holiday to pressure more to facilitate his sale.
Tottenham earlier rejected an offer of £100m plus one from Raheem Sterling, Gabriel Jesus or Aymeric Laporte.
Manchester City are expected to return to try to sign Harry Kane for a larger sum but it would be difficult to accept a payment of 160 million pounds.
Kane scored four goals in Euro 2020 with England, in which he lost the title to Italy on penalties.