Kane has had a three-week break after assisting England to reach the Euro 2020 final.
Spurs have not explained why the 28-year-old did not turn up.
It is understood that Kane felt he had a gentleman’s agreement with Tottenham chairperson Daniel Levy that he could leave the club this summer.
A pre-Euro 2020 move did not materialize as he thought, but Manchester City remains keen on signing the England captain.
Kane’s contract with Spurs runs until 2024 after he signed a six-year deal in 2018.
He scored 23 top-flight goals last season to claim the Premier League Golden Boot for a third time, having initially won the award in 2015-16 and 2016-17.
He also has 221 Tottenham goals to his name, which puts him second in their all-time goalscorers’ list behind Jimmy Greaves, who scored 266 times for the club between 1961 and 1970.
Spurs play Chelsea and Arsenal in high-profile friendlies this week, and new manager Nuno Espirito Santo has actually spoken optimistically about the prospect of working with Kane.
Speaking at his first news conference after being appointed as manager, Nuno said last month: “Harry is our player. Period. No need to discuss anything else, I am looking forward to him joining the group.
“Harry is one of the best players in the world. That is all I need to say.”
‘Winning trophies is the attraction for Kane’ – analysis
Without an official explanation for why Harry Kane failed to turn up, there is room for misinterpretation. Did Kane have an agreement from his club to stay away or was it his own doing?
Moreover, given he was expected to be at Tottenham for Covid testing and there has been no legitimate reason put forward for why he wasn’t, it seems clear Kane wants out of Tottenham – and he wants in at Manchester City.
City won trophies last season – Premier League and Carabao Cup – which is the attraction for Kane. He supplies guaranteed goals as a number nine, which is the attraction for City.
Obviously, the fee is not a problem. Neither are the wages. The city has operated well within Financial Fair Play limits for some time now. And while Sergio Aguero had been reduced to a peripheral figure in Pep Guardiola’s squad by the end of last season, he remained one of their highest earners.
In addition, it is expected at least one senior squad member – probably Bernardo Silva – will leave this summer if, as seems highly likely, Kane and Grealish arrive.
The big unknown is the thoughts of Tottenham chairman Levy.
Of all Premier League executives, he is the least known candidate to cave into player power.
But Levy did say in June that Tottenham had to be ‘sensible’ in the transfer market this summer.
They have already spent £20m on one player, are set for another near £50m outlay on another in Atalanta defender Cristian Romero, and have been strongly linked with Fiorentina’s Dusan Vlahovic, In as much as the 21-year-old Serbian striker would also cost over £40m.
Is that the kind of sensible spending Levy was talking about – or is it getting new arrivals in ahead of an important departure?
Without clarity on his absence, it is impossible to know for certain, but the debate around Kane will only get louder for the fact he is not there.
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