Kane has always maintained he is happy at Spurs but Pochettino says Philippe Coutinho's move from Liverpool to Barcelona shows there can be no room for complacency.
Tottenham's star striker underlined his value again on Sunday by scoring twice in a 3-0 win over AFC Wimbledon as Pochettino's side eased into the FA Cup fourth round.
Jan Vertonghen's first club goal since October 2013, a sensational 30-yard strike, added some gloss late on at Wembley.
But, asked afterwards if Kane might break the mold of players leaving for the world's biggest teams, Pochettino issued a note of caution.
"Harry is so special," said Pochettino. "Because he loves Tottenham and he has always been at Tottenham.
"But we need to be clever how we manage him. The player needs to choose to stay here, you cannot force the player to stay here.
"Our job is to try to work together and try to achieve everything we want at the club and of course Harry is such a special player. I told him only a few special players can spend all their career in one club.
"I think Harry is this type of a player who can stay all his career at Tottenham because he loves Tottenham, but in football you cannot be sure.
"It is today, the present. Tomorrow and after tomorrow you need to doubt. That is why it is so important to work together and try to achieve all that you want."