The England international scored twice in his side's 4-1 win over Liverpool at Wembley on 22 October. He was replaced by Fernando Llorente in the 88th minute and was seen leaving the field clutching his hamstring.
Pochettino had earlier played down any injury concerns after his side's league win over the Merseyside club. The Argentine manager even confirmed the 24-year-old will be rested for the Carabao Cup clash against West Ham United at home.
Tottenham suffered a 3-2 defeat to Slaven Bilic's side and are out of the Carabao Cup. Following the north London club's latest defeat, Pochettino refused to confirm if Kane would be able to face United at Old Trafford on Saturday.
When asked by beIN Sports if Kane would be ready to face Jose Mourinho's side, Pochettino said: "We'll see, we'll see."
"We need to assess the team because we were forced to rotate for different reasons and we'll see what happens in the next few days."
Kane has been in fine form for Tottenham this season, scoring 13 goals in 12 appearances in all competitions this season. This also includes five goals in the Champions League from three starts.
The striker's potential absence could be a blow for Spurs, especially when Pochettino is looking for a reaction against United following their Carabao Cup defeat. The ex-Southampton manager saw his side surrender a 2-0 first-half lead to suffer a 3-2 defeat to West Ham. Pochettino expressed his disappointment with his side's second half display on Wednesday.
"I feel very disappointed because in the second half we were a different team from the first half. We lost focus and allowed them to come back into the game," the Spurs manager was quoted as saying by the club's official website.
"It's difficult to explain. We must fight and be aggressive until the end. We lost the game for different reasons and now we have to be relaxed, calm, try to analyse why and then try to be competitive against Manchester United on Saturday."