Kane drew level with the late Jimmy Greaves when scoring his 266th goal for the club to seal a 1-0 victory over Fulham in the Premier League on Monday.
But assistant head coach Cristian Stellini (48) said that he has struggled to train this week.
"We only have one problem with Harry, with illness this week and he hasn't trained much. He trained today but we have to think about this," he told a news conference.
"We know that Harry wants to play every game so we are happy but we have to take care."
It could open the door for new on-loan forward Arnaut Danjuma (25) to make his debut after his move from Spanish club Villarreal on Wednesday.
"He is a player that can play like a striker or a winger. He has a lot of positions he can cover. So we are happy and we are looking forward to working with him," Stellini said.