The England captain suffered injuries to both ankles during the 3-1 defeat to Liverpool last week and Spurs feared he would face an extended spell on the sidelines.
But the 27-year-old has made good progress and Mourinho expects him to be fit to face either Everton in the FA Cup or for the Premier League trip to Manchester City next week.
Kane has scored or assisted 23 of Tottenham’s 34 Premier League goals this season.
“Good progress, he’s happy with the progress and of course we’re happy too,” Mourinho said on Wednesday.
“I think it’s not a very optimistic thing to say next week he should be playing, it will be just a consequence of his good evolution.
“So we’re happy. We were scared when it happened but next week we play Everton and City at the weekend. I believe for one of these matches he should be back.”
Spurs, who face Mourinho’s former club Chelsea on Thursday, have stumbled after a good start to the season and are six points adrift of the top four.
– Alli return? –
With Kane sidelined, Tottenham might benefit from having Dele Alli involved more often and Mourinho revealed he had found “common ground” with the out-of-favour midfielder.
Mourinho said he had a productive meeting on Tuesday with Alli, who has been frozen out this season.
The club blocked a loan move to Paris Saint-Germain during the January transfer window, which the England midfielder, who is carrying an injury, was unhappy about.
“He needs to recover from his injury, he needs to be back to training and have a fresh start,” Mourinho said.
“Because in the last few weeks he couldn’t even train. So that’s the most important thing.
“It’s an important period of the season for the team and for him also. We need him. We need a good Dele Alli.”
Mourinho said his faltering side were missing some “magic” in the attacking areas without Kane, Giovani Lo Celso and Alli.
“Of course, a conversation doesn’t make miracles or put a player in great form without limitations in terms of fitness,” he added.
“But I believe the conversation was maybe the extra motivation he needed to be back as soon as possible and become available for the team.”
Mourinho has revealed that Serge Aurier will return to the squad having been left out for the Brighton defeat following rumours of a dressing-room spat at half-time of the Liverpool match.
Mourinho, who won three Premier League titles in two spells at Chelsea, described new Stamford Bridge manager Thomas Tuchel as a good fit for his old club.
Tuchel was sacked by PSG in December before replacing the axed Frank Lampard as Blues boss last week.
“He was coming from a league that you cannot compare with the Premier League but he is used to working with players of high calibre, used to dressing rooms with important players. He will fit well in a club like Chelsea,” he said.