Kane suffered an ankle injury while attempting to tackle Fabian Delph in the first leg of Spurs' Champions League quarter-final clash with Manchester City.
Tottenham went on to win that tie, but they have been without Kane ever since.
Lucas Moura's hat-trick helped Spurs overcome Ajax in dramatic circumstances in the semi-final of the competition and Pochettino says there is hope that Kane will be ready to take to the field in Madrid.
"Kane is training, he's in a good phase of recovery," Pochettino said at the Bilbao International Football Summit.
"We hope he's there to help, whether that's from the start, off the bench or as moral support in the dressing room. We're optimistic that he can be there to help on the pitch."
However, they have since been able to battle their way all the way to the final, with the likes of Lucas, Heung-Min Son and Fernando Llorente all playing a part in Kane's absence.
"No one was optimistic when we started the group stage with one point," the Argentine added.
"We've been through very hard situations and the team has showed character. You don't eliminate [Manchester] City or come back against Ajax by chance. This gave us strength.
"The start of the season was difficult, especially when we had to go back to playing at Wembley [Stadium]. The fans wanted to move to the new stadium. We suffered a lot; it seemed like the stadium would never be finished.
"The negativity invaded us a bit, but the people made a great effort to come back. It's a great lesson for many people. When you go through what we did for 10 months, you can understand the tears in the semi-final."
Spurs will face Liverpool at Atletico Madrid's Wanda Metropolitano stadium on June 1.