Kane had to be carried off on a stretcher after scoring the winner against Sunderland on Sunday and the 23-year-old looks set for a lengthy spell on the sidelines.
Spurs insist a more accurate diagnosis is not possible due to swelling around Kane's right foot but grade two ligament damage could put the forward out for six to eight weeks.
"He got a ligament ankle problem and we need to assess every day and see," Pochettino said.
"Today it's impossible to give a time for a recovery. I am not a doctor. I can only explain what the doctors said to me.
"He is in a very good mood. We chatted before in the restaurant, he's in a very good way.
"There are different rumours, we cannot guess whether it's eight weeks, 10, four, one. It's impossible to assess today and know how long."