The 24-year-old has not started any of the Saints' three Premier League games so far this season and Fulham boss Martin Jol is believed to be monitoring his situation.
However, Pochettino has claimed that he is unaware of any interest from the Cottagers and stresses that he will not be selling his fringe players, indicating that Cork still has a role to play at the South Coast club.
"I don't know anything about that," Pochettino told reporters. "There's no offer from Fulham, I don't know anything about what you're saying.
"He's a 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."