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Tottenham remains top of the Premier League on goal difference despite being held to a goalless draw by another of its London neighbour, Chelsea, last time out.
Kane played the full 90 minutes at Stamford Bridge but appears a doubt for the derby with 14th-placed Arsenal.
Revealing that Erik Lamela, Carlos Vinicius and Sergio Reguilon also have injuries, Mourinho said: "Lamela is an injury from three weeks, a month.
"I don't believe he has a chance for the weekend. Harry, Vinicius and Sergio - there is a chance for the weekend.
"I'm not going to tell you the nature of his [Kane's] injury. I think he has a good chance [of playing against Arsenal].
"I don't want to lie, I don't want to hide anything in relation to is he going to play or not? I think he's going to play. That's my feeling is that he's going to play."
Kane has seven goals in 10 Premier League games this season and is converting 66.67 per cent of his big chances, per Opta data.
His strike partner Son Heung-min has fared slightly better, finding the net with 70 per cent of his big chances.
Spurs can secure progression to the last 32 against LASK, with Mourinho adamant that the looming derby will not impact his team selection.
"Arsenal doesn't come into our thinking. When you make changes, you make changes based on problems that we had," said Mourinho.
"When we do that, we put trust on the players we have. We don't weaken the team because the Premier League match is next."
