The 26-year-old joined from Plymouth just over three years ago but his time at St Mary's has not always been plain sailing. Puncheon spent several loan spells away from the club after losing his place in the first team and little over a year ago took to Twitter to criticise Southampton executive chairman Nicola Cortese.
The pair patched up their differences and he has now become an integral part of the team. And speaking through a translator, Pochettino said: "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."
The Argentinian added: "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."
On Sunday Puncheon will be coming up against the man that first brought him to St Mary's. Alan Pardew managed Saints for a little over a year and the Newcastle boss has previously been linked with a move for the winger.
Asked how he would reacted if approached by Magpies boss about Puncheon, Pochettino said: "I wouldn't be able to do anything if that were the case. It will be down to the player to make that decision. I've said before that we will make decisions on the future."
Puncheon is one of several players, including Rickie Lambert and Jose Fonte, that were brought to Southampton by Pardew. However, Pochettino, much like predecessor Nigel Adkins before the home match with Newcastle earlier in the season, says he owes the former boss nothing.
"I always think that in football is not just one person signing any one players," he said. "It is the club signing the players. Now I am the manager here and I will probably bring in some players."
Reports in Spain suggested one player that Pochettino had hoped to bring in during the January transfer window was Getafe's Abdelaziz Barrada. It was claimed the Saints failed with a club-record £15.25million bid for the midfielder, who has been linked to Barcelona and Real Madrid.
"There is no truth to that," Pochettino said. "Nothing of the sort has happened. "On a personal level, I have not made any offers, any approaches, for any players."
Source: PA
Source: PA