Kane informed Spurs of his desire to leave north London this summer in search of trophies earlier this summer, with Premier League champions City his preferred destination.
Chairman Daniel Levy stated last month that 'what other clubs want is not always possible to achieve' when speaking to Tottenham's official website on the topic of players who might be the subject of bids in the transfer market.But The Sun claim Levy has agreed to let Kane join a Premier League rival following a U-turn he announced last week, with the England captain reportedly set to earn £400,000 per week at the Etihad Stadium.
The same outlet claims Levy rang Kane and and his elder brother and agent Charlie, 32, to tell them on Friday that he had changed his mind about only letting him leave for a club in Europe.
The report adds the length of Kane's deal at City has yet to be decided but that it will either run for four or five seasons.
Reports last month suggested Spurs had rejected a £100m bid from City for Kane and boss Nuno Espirito Santo revealed last week he was confident Kane would be committed to the cause.
Director of football Fabio Paratici was also keen to rebuild a team involving the forward, but the latest reports suggest he will be making a move up north to play under Pep Guardiola.
Kane's desire to leave followed another trophyless campaign for Spurs', who were defeated by City in April's Carabao Cup final.
The 27-year-old appeared to put that disappointment behind him by netting four goals at Euro 2020 to help England to the final of the tournament before more heartbreak arrived in the form of a penalty shootout defeat by Italy.
A move to City this summer would see him link up with Three Lions team-mates Kyle Walker - also a former Spurs colleague - centre-back John Stones and forward Raheem Sterling, with whom he combined so well with at the Euros.
The Sun however claim City and Brazil striker Gabriel Jesus could be a replacement for Kane at the north London outfit.
The reported £160m fee would see City smash the English record transfer fee, which is currently the £89m Manchester United paid Juventus for Paul Pogba in 2016.
The transfer would also be a Tottenham record, with the reported figure for Kane way above the £86m they recouped for Gareth Bale when the Wales star joined Real Madrid in 2013.