Speaking after his side's loss to Norwich City, the Saints boss revealed he has no plans to sell the former England U21 international, despite reported interest from Fulham
The former England U21 international was left out of the Saints side that fell to a disappointing 1-0 defeat at Norwich City on Saturday and has only one minute of Premier League football to his name so far this campaign.
But, speaking after the match, Argentine boss Pochettino insisted that Fulham had not tabled an offer for the midfielder, before declaring that Cork was not for sale in any capacity.
"There has been no offer from Fulham," Pochettino told reporters. "I know nothing of any offer from Fulham.
"I make decisions for the best of the team. He's not injured. Why he was not involved is an obvious answer."
When quizzed over whether he would be prepared to sell Cork, Pochettino responded: "He’s a valued first-team squad member, he’s a part of this team.
"If we start selling players we’re only going to be left with just 11 players, so no."
Southampton lost at Carrow Road thanks to a second-half winner from Nathan Redmond, although skipper Adam Lallana could have given the visitors the lead after hitting the post.
Pochettino and his men take on West Ham at St Mary's in their next Premier League encounter, which comes after next week's international break.