Kane underwent surgery after suffering the injury against Southampton on New Year's Day, and he was expected to be back in April.
However, per Goal's Patric Ridge, Mourinho identified their penultimate Premier League match of the season on May 9 as his likely return date:
"The Leicester match. Maybe we need that match for something. To be fourth, to be fifth, to be sixth. Maybe he can help us in this match. I hope. Is that the best-case scenario at the moment? Yes, I think so."
Such a return would mean Kane is back in time for the FA Cup final or the UEFA Champions League final should Spurs make either of them, although he'll be lacking fitness.
Kane shared a glimpse of his rehabilitation process on Twitter near the end of January:
The striker is the focal point of Spurs' attack, and he had contributed 17 goals and two assists in his 25 appearances for the club this season.
Spurs blogger Chris Miller offered further insight into his importance to the club's attacking output:
Tottenham did not manage to bring in a striker to cover for the 26-year-old in the January transfer window, but they did sign winger Steven Bergwijn, who can play on either flank or through the middle.
He netted a fine goal for the Lilywhites on his debut as they beat Manchester City 2-0 on Sunday:
It was only his seventh goal of the season in all competitions. He netted six in 29 matches for PSV Eindhoven prior to his move, so he's unlikely to replicate Kane's goalscoring contributions.
He also laid on 13 assists in that time, though, so he should be able to provide Heung-Min Son, Dele Alli and Lucas Moura with more ammunition.
Kane's delayed return will also be a significant concern for England ahead of UEFA Euro 2020. The Three Lions captain has bagged 13 goals and six assists in his last 11 games for his country.
Gareth Southgate has a variety of goalscoring options to call upon including Marcus Rashford—albeit he will also be working his way back to fitness before the end of season with a back injury—Raheem Sterling and Jadon Sancho, but leaving Kane out would be a big call even if he's not fully fit.