The England captain suffered an ankle injury in Spurs’ quarter-final clash against Manchester City, which at the time appeared to rule him out for the remainder of the season.
Pochettino, though, offered some hope that his star man could return from the injury in time for a potential appearance at the Wanda Metropolitano, if Tottenham make it that far.
"We'll see. Yesterday we were talking. We will see what happens," Pochettino said on Saturday when asked if Kane would be fit to return by the end of the season.
"If you said to me he is going to be available for the second leg in Ajax or the last [Premier League] game against Everton, I don't know.
"For sure it is going to be difficult. If we are capable of beating Ajax and be in the final in June 1 then maybe yes. Yesterday we were talking about that, we'll see.”
Tottenham's preparations for Tuesday's semi-final first leg were far from ideal, as they went down 1-0 at home to West Ham in the Premier League on Saturday.
With Kane missing, Pochettino began the game with a frontline of Heung-min Son and Lucas Moura, but the pair were regularly thwarted by the Hammers’ Lukasz Fabianski through the match.
Tottenham's league defeat opened the door for Arsenal and Chelsea to close the gap in the race for a top-four finish, while Manchester United - who face Maurizio Sarri's side on Sunday - also remain in with a chance.
However, Spurs will now turn their focus to the Champions League, and their first semi-final in Europe’s elite competition.
The Dutch side had their Eredivisie game against Vitesse moved to Tuesday night, in order to give the Amsterdam outfit more time to prepare for their midweek trip to London.