Puncheon, who spent spells out on loan with Millwall and Blackpool last season, is widely expected to be on the move this summer having fallen out of favour at St Mary's.
The former MK Dons, Barnet and Plymouth player's agent, Tony Finnigan claimed last week that he had fielded a call from Pompey regarding his client.
However, Fratton Park boss Cotterill insists that the source of the contact was in fact from Puncheon's camp and that if he was interested in the 25-year-old, he would speak directly to Saints.
While the South Coast chief was keen to stress he did not instigate any previous discussions, he stopped short of ruling out any future interest in the wide man.
He told The News: "Our policy is not to discuss targets but it always seems speculation comes out somewhere. It is usually from the agent or someone to do with the other club, it is never driven by us.
"On this occasion I have read Jason Puncheon's agent saying we have made an enquiry. Well, we have not made an enquiry. We have not even made a phone call - but we received a phone call.
"Our physio knows Puncheon, Hayden Mullins knows Puncheon, he's a good, young player but that is as far as it goes at this moment in time.
"If we do make an offer we would contact Southampton Football Club directly. Let's just say we have not. Whether we will do, I don't know the answer to that at the moment.
"But Portsmouth have not made contact about Jason Puncheon. Someone has contacted Portsmouth, though."