Manager Mauricio Pochettino told reporters on Friday that the England worldwide saw a specialist on Thursday after damaging his hand when he fell heavily in their 1-0 win over City in the first leg of their quarter-final clash on Tuesday. He broke his hand in two parts.
All three are continuing on-field rehabilitation and the club are hopeful they will be back available for selection soon as Tottenham continue to fight for a place in the top-four and a spot in the Champions League semi-finals.
"We need to assess him every day but [we need] to have proper answers to see when he possibly can start training with the team, but today it is impossible to give a date".
The Argentine also stressed that his team will cope with the absence of Kane by equally sharing the responsibility in attack among themselves during the remaining games of the season.
Pochettino could be forced into changes following that rigorous European tie: "Tomorrow is not to rest players, but to take the best decision after the big victory over Manchester City", he explained.
Tottenham boss Mauricio Pochettino has hinted Dele Alli could miss their Champions League quarter-final second leg at Manchester City.
Blue Jackets rally from 3-goal deficit to beat Lightning 4-3
Subban, Ryan Johansen, Roman Josi and Filip Forseberg, again all guys that have been here before and know how to get things done. Once Dallas scored, their body language changed and they were decisive, which led to them building a 3-1 lead.
Even if he is deemed fit to play Pochettino will surely not want to risk him ahead of Tuesday's game. "It was a hard moment for him".
"We are maybe going to do some situations to help". He had a scan yesterday.
"It's true that now we can have an opinion that it was a challenge with not too much need for it", added Pochettino.
When asked whether he believed Kane could return this season, Pochettino said: "We'll see, there is five weeks, it is going to be hard".
"I am not optimistic, but we'll see". It's a lot of coincidence.
Meanwhile the likes of Serge Aurier (hamstring), Eric Dier (hip flexor) and Erik Lamela (hamstring) are out of the Huddersfield fixture.