The England striker has been out of action since injuring his ankle in the 1-0 win over Sunderland in mid-September, but Pochettino says he is nearing a first-team return.
Toby Alderweireld is also close to full fitness after overcoming the knee problem he suffered against West Brom two weeks ago.
"Harry is not ready yet.
"It's difficult to know but we'll see. His evolution is great. Maybe for Sunday, perhaps the Champions League.
"Frustrated is a word we don't use here. Both (Kane and Alderweireld) are positive. Of course they want to be back playing quickly - not least because we push them hard in training. Injured players have it much tougher than the fit ones."