The Sun reports how the 29-year-old travelled to the Spanish city with his family at the weekend, after being given an extended break by Michael Laudrup to recover from recent international commitments.
His arrival in Barcelona prompted speculation he had agreed to meet with Nou Camp representatives to discuss the possibility of a move when the transfer window reopens in July.
Tito Vilanova is believed to be in the market for a new number one, as Victor Valdes approaches the final year of his Barcelona contract.
However, any suggestions that Vorm is being lined up as the Spanish stopper's successor have been played down by the side from South Wales, who will be hoping to retain the Holland international's services next season.
Gunners boss Arsene Wenger has also been credited with an interest in bringing Vorm to the Emirates Stadium, but Arsenal could face further competition for the player's signature from Liverpool.
Former Swans manager Brendan Rodgers is equally keen to add the Dutchman to his Anfield squad, and be reunited with a player he brought to the Liberty Stadium in a £1.5million deal in 2011.