Martin Jol has already bolstered his midfield ranks in the transfer window with Derek Boateng and Scott Parker, but had reportedly earmarked Chelsea academy graduate Cork as another potential signing.
Cork has played just five minutes of Premier League football so far this season, appearing as a late substitute in his side's opening-day win over West Brom.
However, Pochettino insists the 24-year-old has a future at St Mary's Stadium, despite seeing Victor Wanyama and Morgan Schneiderlin preferred to him so far this term.
"There's no offer from Fulham, I don't know anything about (this)." the Argentinian said.
"He's a first-team squad member, he's a part of the team, if we start selling players we will just be left with 11 players.
"We will see what happens from here until Monday (transfer deadline day). That's a long time and we can make a lot of decisions, but like us the rest of the clubs are also looking to add to their squads or have players leave, so we will see what happens.
"There are a couple of areas that perhaps we need to reinforce, but there's a couple more days for us to make decisions."
Pochettino also lamented young full-back Luke Shaw's call-up to the England Under-21s squad to face Moldova and Finland.
The 18-year-old has previously been called up to three U21 squads, but has been forced to withdraw each time through injury.
And his club manager has admitted he would prefer to keep Shaw on the south coast to keep a closer eye on his development.
"I would prefer for Luke Shaw to stay with us and work with us (rather than going to England Under-21s), but we'll see what the decision is," he added.
