The 28-year-old was due at Hotspur Way on Monday after being given an extended break following England's run to the final of Euro 2020 but failed to appear as he tries to force through a move away from the club.
Manchester City are the front-runners for his signature -- with Manchester United and Chelsea also monitoring the situation -- but Spurs do not want to part with their prized asset, who they value at around £150 million.
Kane believes he has a gentleman's agreement to leave Tottenham this summer, creating a standoff that has been exacerbated by his decision not to return as originally planned.
Spurs and the player have differing views over the situation. Sources claim Kane feels his plans were communicated to the club and therefore the present furore has been blown out of proportion, but Spurs are thought to be disappointed by his actions.
No decision has yet been taken but sources have told ESPN that Spurs could begin internal disciplinary action against Kane, leading to a fine of perhaps as much as one or even two weeks' wages.
Kane has three years remaining on his £200,000-a-week contract but wants to leave Tottenham in pursuit of silverware. He is one of the Premier League's finest strikers, having scored 166 goals in 245 games, but is yet to win a trophy for club or country.
City want to sign Kane but are yet to offer a package that would make Spurs chairman Daniel Levy soften his stance.
Kane was due to report for COVID-19 testing and routine blood work on Monday ahead of a return to training on Tuesday but is now expected to return this weekend, having been on holiday in the Bahamas.
Tottenham's preseason preparations continue this week with a trip to face Chelsea on Wednesday before a north London derby against Arsenal on Sunday.