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The striker looks certain not to be involved in the Premier League home match against Southampton after suffering an ankle injury in last the 2-2 draw with Everton.
Caretaker manager Ryan Mason, who took over from the sacked Jose Mourinho on Tuesday (AEST), could offer no guarantee the England captain would be ready for Sunday's Wembley trip.
"I'm not sure currently. He didn't train today. It's one of those cases of taking it day by day. We're still not sure about the weekend just yet,' he said. "What we do now is Harry's working extremely hard to get over this injury."
Kane has scored 31 goals and had 16 assists across all competitions this season, making him the only player from Europe's 'top five' leagues to score 30 or more times and add at least 15 assists.
Handed the job until the end of the season, rookie manager Mason is a former Tottenham player who had to retire three years ago due to a head injury sustained while at Hull City.
The 29 year-old said he was "very proud" to be chosen to lead the team, and rallied the players by declaring: "I want us to be brave and aggressive and play like Tottenham Hotspur."
Chairman Daniel Levy proposed Mason should succeed Mourinho as interim boss after dismissing the former Chelsea and Manchester United manager.
"We had a very long conversation," Mason said. "I took training, we had another conversation and he asked me if I wanted it."
Former Charlton Athletic and England defender Chris Powell and ex-Watford man Nigel Gibbs will be assistants to Mason.
Mason said he and former Spurs boss Mauricio Pochettino had "exchanged a few messages" since the dramatic upheaval. He also said he had not spoken to Mourinho.
Mason was in the line-up the last time Saints won at Spurs in the Premier League, a 2-1 victory in May 2016, but Tottenham have typically had Southampton's number in north London, winning eight of their past nine at home in this fixture.
Tottenham's impressive record in home Premier League games on Wednesday is another positive omen as Mason seeks a winning start. Since a 1-0 loss to Leicester City in January 2016, they have won 10 of their 11 such matches (D1), scoring 25 goals and conceding just four.
Son Heung-min scored four goals in Tottenham’s 5-2 win against Southampton in the reverse fixture earlier this season, with all four assisted by Kane. That remains the only occasion in Premier League history when a player has scored four goals in a match with each of them assisted by the same player.
Mason will have plenty to think about as he prepares to boss a team in a Premier League game for the first time, a situation he had not seen coming and described as "crazy".
The man who joined Tottenham's academy as an eight year-old, going on to reach first-team level and England selection, is determined to take the change of circumstances in his stride.
"It's football," he said. "Anything can happen. You just have to be ready for what football can throw at you at times."