The Tottenham star is being heavily linked with a move away from north London due to having just one year remaining on his contract at the club.
With Bayern Munich interested, the 29-year-old could have the opportunity to join a European powerhouse, but a move across London could also be appealing.
Kane was a star man under Pochettino during their years together at Tottenham and after taking charge at Stamford Bridge, the Argentine boss has admitted that he could be in the market for a new striker.
He said: "We'll see. It depends on the situation and the circumstances. We are working. Football is really dynamic. What we have today maybe disappears tomorrow.
"We need to be ready to … [if] we need more or not. Or maybe we go to the pre-season and we realise that we need to improve in different positions or add more players that can score, or we have enough.
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"It's really dynamic and we are going to assess every day the situation."
But when quizzed on the prospect of a move for Tottenham's all-time top goalscorer, Pochettino delivered a coy, but complimentary response.
"I don't like to talk about players in another club, but you are talking about one of the greatest, one of the best strikers in the world.
"It's not fair to talk, it's not fair to say nothing.
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"People are not stupid, fans are not stupid, they are so clever and they know my relationship with him was always amazing.
"I saw him when he was young, grow up and achieve all he was achieving and of course we have a great relationship."