But Pochettino, who has admitted Kane can not be forced to stay, believes the 24-year-old would prefer success at Tottenham over any other team.
"I've always said, just keep progressing, keep getting better", Kane said.
Additionally, fellow 25-year-old Son is a priority for Spurs, having seen the South Korean hit 10 goals in all competitions this term, continuing to impress after notching 14 Premier League goals last season.
"Of course, the chairman is the man who manages everything and in the end takes all the decisions", Pochettino said ahead of Tottenham's Premier League match against Everton on Saturday.
He appeared to leave the door open to a possible transfer earlier this week when he said his willingness to stay at Spurs would depend on their ability to win silverware.
"I'm 100% confident. Every single player that we want to keep, I can assure you will be playing for Tottenham Hotspur next season", he told Sky Sports. "Personally, I never look next to me at what another team is doing. It's about how I believe and try to make things happen".
"You know better than me that if you want to sign players to help you, there must be an opportunity and it's hard to find this opportunity", Pochettino said.
More importantly, Tottenham will have the chance to put some pressure on fourth in the table Liverpool and Arsenal, who are sixth in the standings.