Spurs, who host Newcastle United at Wembley on Saturday, are third in the Premier League and seven points behind leaders Liverpool with 14 games remaining.
Kane, the North London club's top scorer with 14 league goals this season, is expected to be out until March after damaging left ankle ligaments against Manchester United at Wembley on Jan. 13.
The player recently posted a video on Twitter showing himself in light training, raising hopes he might be back sooner.
"I cannot tell you if he is ahead of the schedule or not. We assess him day by day," Pochettino told reporters.
"He is showing on social media that he looks very strong and very fit and very well, running and doing some exercises. He is very strong and is a guy that puts in 200 percent to try and be back as soon as possible.
"We'll see. We need to assess day by day, week by week, but we are happy in the way that he is recovering."
Pochettino said England midfielder Dele Alli, who is also expected to be out until March with a hamstring injury, was also doing well.
(Reporting by Alan Baldwin; Editing by Toby Chopra)
