Kane has been ill along with other players and staff, but Conte denied there was a food poisoning outbreak.
Fourth-placed Spurs will qualify for the Champions League if they win at Norwich City on Sunday (16:00 BST).
"In this moment, this virus is the last of our problems," said Conte. "We are close to a big achievement."
England captain Kane, 28, has scored 16 times in the Premier League this season - five fewer than team-mate Son Heung-min - including four in his past four top-flight appearances.
He was reportedly due to attend a media event on Friday, but withdrew as a precaution.
"Yes for sure [Kane will be fit], and because in the last game we had Dejan Kulusevski and he didn't train on Saturday, but was good to play," said Conte.
"Harry doesn't want to miss this type of game."
Conte said there had been "three or four cases of stomach problems" surrounding Tottenham's previous match, a 1-0 win over Burnley on 15 May when Kane scored a decisive penalty.
"In this week I have to be honest, we had a couple of cases but we overcame the situation," he said.
"Also members of the staff, one day they were not feeling so good. I don't know why, the last week but also this week, we faced this situation."