Kane suffered another ankle injury in the 2-2 draw at Everton last week and missed the midweek win over Southampton.
Interim boss Ryan Mason does not know whether the England captain will be available for Sunday’s showpiece game against City at Wembley as Spurs hunt their first trophy since 2008.
“We’re not sure yet. He didn’t train with the team today (Friday) but we’ll have more of an idea tomorrow to see if we can get him back on the pitch,” said Mason, who replaced the sacked Jose Mourinho on Monday.
“It’s a case of taking it hour by hour now. So the days are obviously running out. It’s a case of seeing how he feels in the next four hours, the next six hours, and go from there.”
Kane has a habit returning quickly from injuries, notably for the 2019 Champions League final, in which he was well off the pace in a defeat against Liverpool.
This ankle problem is not as serious but Mason said Kane would not be risked if it could inflict further damage.
“A week without training is not a problem for someone in Harry’s condition,” he said.
“But I think we are going to have to assess it later tonight, early on tomorrow morning, and see if we can get him onto the pitch.”
Mason, 29, finds himself in the incredible position of leading his boyhood club out at Wembley for a cup final, capping a whirlwind week dominated by talk of the ill-fated European Super League.
Mason, who had to retire aged 26 after suffering a fractured skull playing for Hull, was in Tottenham’s squad when they were beginning to challenge for titles under Mauricio Pochettino.
Pochettino took Tottenham close to ending their trophy drought on several occasions but failed to deliver silverware.
Asked whether Spurs should have won a trophy during that time, Mason said: “I think there was probably a two or three year period when Tottenham had chances, they maybe should have, but football doesn’t always work out like that.
“What they did do, they developed a great team. And the club went in a direction that we wanted, and everyone within the club wanted that.
“That’s how Tottenham should go about things. Unfortunately we didn’t get over the line.
“But if we don’t get over the line on Sunday, we still have our identity and our DNA as a football club. And that’s the most important thing.”