Kane is in the early stages of rehabilitation following surgery to repair a ruptured tendon in his hamstring, and there is still a long way to go with his recovery, but Mourinho's latest comments are a big positive.
Spurs have previously stated they expect him to return to training some time in April, though medical experts have said an injury like that could keep him out for six months.
The England captain, fighting to get fit for Euro 2020, is a notoriously quick healer and posted a video on Twitter last week of him stretching.
He has flown to the Bahamas this week for a stint of warm-weather training, amid hopes he could be back soon.
Mourinho insists nothing has changed from his initial prognosis and expects to have his striker back for the end-of-season games against Leicester and Crystal Palace in May.
And with a thrilling four-way battle for one Champions League qualification spot unfolding, Mourinho hopes Kane's recovery could be timely.
Asked if his talisman would play again this season, the Portuguese replied: "The Leicester match (May 9). Maybe we need that match for something. Maybe we need that match for something.
"To be fourth, to be fifth, to be sixth. Maybe we need that match for something and maybe he can help us in this match. I hope."
Mourinho then added there have been no setbacks and the player is continuing with his treatment plan in the hope he will play again this season, which of course would also be a huge boost for England boss Gareth Southgate.
Spurs will be hoping Kane might be back to help them win a possible FA Cup final in May, but they will need to get past Southampton in Wednesday's fourth-round replay first of all.