Kane suffered ankle ligament damage in a 4-1 Premier League win away to Bournemouth earlier this month, ruling the centre-forward out of the subsequent trip to Swansea in the FA Cup and causing him to miss England's friendly meetings with Netherlands and Italy.
Spurs travel to face Champions League qualification rivals Chelsea this weekend at Stamford Bridge, where a victory for the away team would see them move eight points clear of last season's title-winners.
But it remains to be seen if Kane will be risked for the showdown with Antonio Conte's side.
"He is doing well and improving every day," Pochettino told a news conference.
"We need to assess him, it is still a few days until the game.
"It is difficult now to say if he will be involved this weekend - I cannot say no and I cannot say yes – but maybe next weekend.
"We are positive about his recovery and we are happy. After Bournemouth, everyone thought it would be a long period out."
Tottenham star Dele Alli was a notable absentee from England's starting XI over the past week, the attacking midfielder only coming on in the second half of the 1-0 win in Amsterdam.
He was an unused substitute for the 1-1 draw with Italy at Wembley, and Pochettino knows the 21-year-old may need some encouragement after being overlooked by England boss Gareth Southgate, seemingly jeopardising his prospects of a starting role at the World Cup.
"With Dele my relationship is always very good, like all the players here in Tottenham," he said.
"Of course, it's always not only advice, it is talk aimed at trying to help the players, to help the players when they need to be pushed.
"I think my job is to try to help the player to [achieve] what they deserve and what they want - giving them the tools to perform. That is one of my jobs."
Asked about the likely reason for Alli's England demotion, Pochettino said: "I don't know. I cannot give opinions about a context that I wasn't there for.
"The national team has their context, and Tottenham has a different context. I wasn't there. Only I can talk for myself, how he is at Tottenham, and we try to help him to achieve what he wants."