The 27-year-old was absent from training this morning ahead of Thursday's Europa League trip to Austrian Bundesliga side LASK with an unspecified injury.
Mourinho refused to elaborate on the exact issue Kane is struggling with but said his top goalscorer and talisman will likely be available for the visit of their fiercest rivals.
"I'm not going to tell you the nature of his injury," Mourinho said at a news conference on Wednesday. "I think he has a good chance [to play on Sunday]. I don't want to lie.
"I don't wide to hide anything in relation to: 'Oh, is he going to play or no.' I think he is going to play. My feeling is he's going to play."
Sergio Reguilon and Carlos Vinicius are also doubts having missed Wednesday's training session while Mourinho said Gareth Bale is still learning to trust his body after being frozen out of the first-team picture at Real Madrid.
Bale has started just five games since rejoining Spurs in September and was an unused substitute in Sunday's goalless Premier League draw at Chelsea.
"The only problem with Gareth is to get the dynamic and confidence of playing consecutive matches without any bad feeling, without any negative feeling, without any remembrance of the recent past where the condition was not the best and the fears were there," Mourinho said.
"I think it is more about that. But he's playing regular, he has a chance of a physical evolution, of course he doesn't need a technical or tactical evolution, he just needs a physical evolution, getting to the intensity of matches and getting his confidence back to play consecutive matches, like three matches in a week. So, I think it's more about that."