Kane suffered a "significant lateral ligament" injury in his left ankle during Spurs' 1-0 Champions League win over Manchester City and, although the club have yet to put a timescale on his return, he is unlikely to play again this season.
When asked whether he believed Kane could return this season, Pochettino said: "We'll see, there is five weeks, it is going to be hard".
That problem kept him on the sidelines for nearly two months, while he missed a month of last season due to a problem with his right ankle and also spent a total of 10 weeks out during the 2016/17 campaign. It's going to be tough.
Despite the absence of injured stars Kane and Dele Alli, Mauricio Pochettino's much-changed side made it three victories from their first three games at the impressive Tottenham Hotspur Stadium. I was speaking to him before and we need to assess every day to properly answer to see when he can come back to train with the team.
"We will see because he is doing some training sessions with the protection and he needs to feel comfortable", Pochettino said.
The ligament damage means the striker will not only miss the rest of Tottenham's Premier League season but will not lead England at June's UEFA Nations League final in Portugal, which will be a huge blow to Gareth Southgate.
Pochettino did not allude as to whether surgery would be needed but did say Spurs have plans in place for Kane's recovery. And we went straight up the other end with a break of our own, only for Kongolo to deflect Llorente's effort wide. The timing of his recovery is still unknown.
But Pochettino has allayed fears he will interfere with any selection of the 25-year-old by England boss Gareth Southgate.
"Today there are a lot of techniques to try to help that and not become chronic and, of course, because we have very good people here", he said. But I don't believe it will be a chronic problem.
"For some of us, they will be the last Premier League games of our lives so we have to try to enjoy it a little bit as well".