Harry Kane, a transfer target for Manchester City, did not return to the Tottenham training ground as expected on Monday morning amid speculation over his future.
The striker was scheduled to have coronavirus testing on Monday before starting training on Tuesday.
Kane has had a three-week break after helping England reach the Euro 2020 final.
Spurs have offered no explanation for why the 28-year-old did not turn up.
It is understood Kane felt he had a gentleman's agreement with Tottenham chairman Daniel Levy that he could leave the club this summer.
A pre-Euro 2020 move did not materialise as he hoped, but Manchester City remain keen on signing the England captain.
Kane's international's team-mate Jack Grealish is also a target for City, who have a made a £100m bid for the Aston Villa midfielder, and he turned up for pre-season training with the Midlands club on Monday.
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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 previously 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 already 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 talk about 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 official clarification over 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?
However, 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.
Evidently, the fee is not a problem. Neither are the wages. City have 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 obvious candidate to cave in to 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, even though 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 a significant departure?
Without clarification 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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