Southampton fans are clamouring for Puncheon to extend his stay beyond the end of the season - something Pochettino would also like to see.
"I myself haven't spoken anything about his contract," the Argentinian said, speaking through a translator.
"I've only recently arrived so my first priority has to be the whole of the team, not just one player.
"There are certain movements that were already happening with players when I arrived.
"In the coming weeks we will be speaking at a club level with the appropriate people to decide on the matters of players at the club.
"Puncheon is a player I am counting on and he is a player that has certain qualities and skills that are good for the team so, yes, I'd like him to stay."