Kane, the Premier League club's leading marksman with 24 goals, sustained the injury during Tottenham's FA Cup win over Millwall this month.
The north London side refused to put a time scale on the 23-year-old's return but media reports had suggested he was set for a lengthy spell on the sidelines.
"He will be fit before the end of the season and we believe he can be available in the near future," Pochettino told reporters on Thursday. "...I cannot provide a time it will take for him to be available again, but I don't think it will be too long."
Pochettino, however, was not as optimistic about defender Danny Rose's recovery from a knee injury. "He is probably a little bit behind Harry Kane, but we are positive. We need to wait to see what happens with the specialist," he said.
Read the full article on eurosport.co.uk: Pochettino: Tottenham's Kane nearing return from injury