The La Liga club's president Sandro Rosell had previously confirmed his hopes of signing Silva, but the 28-year old is under contract in Paris for a further four years having made the switch from AC Milan last summer.
Injuries to Carles Puyol last season meant that Tito Vilanova's side were often short on cover defensively and Barcelona are believed to see Silva as a long-term replacement for their club captain.
The Brazil international impressed in his debut season in France, helping PSG claim the Ligue 1 title, and he says he is happy to honour his current contract.
"I saw the news that I would go to Paris to meet the president and the new manager of PSG to talk about a possible transfer," he told Globo Esporte.
"That won't happen as I will see out the contract I have with the club. I feel fulfilled."