Kane suffered ankle ligament damage in a 4-1 Premier League win away to Bournemouth earlier this month, ruling the centre-forward out of the subsequent trip to Swansea in the FA Cup and causing him to miss England's friendly meetings with Netherlands and Italy.
The north London confirmed on Thursday that Kane had "stepped up his rehabilitation", suggesting he was still not fit enough to return.
Progress is going well for Kane, who should be fit and ready for this Summer's World Cup in Russian Federation.
Any game against Chelsea is a huge tie for Tottenham, yet Sunday's game carries huge importance for both sides.
Both players were involved in worldwide duty this week, and will be checked on before the crucial matchup.
"I cannot say no, I cannot say yes".
He added: "I think to compare with Arsenal, I think it is similar".
"He is doing well and improving every day", Pochettino told a news conference.
"Arsenal, Chelsea are always tough games because they are derbies and for me it is a similar type of opponent and of course for the fans it is so important".
"But the most important is that we are so positive about his recovery". Maybe next weekend. But the most important is that we are so positive about his recovery, and we are doing fantastic, and we are so happy. "But for us three points would put us in a very good position in the table". "I wasn't there. Only I can talk for myself, how he is at Tottenham, and we try to help him to achieve what he wants". I think, when you play this type of game, I think the pressure is for both teams. "That is not what counts".