Dutch magazine Voetbal International reportedly quotes Vorm as saying that it would be "special" to play under Rodgers again.
Vorm told the club's official website: "The comments that came out of the interview from the Dutch press have been lost in translation.
"They asked me about Brendan, and I said I enjoyed working under him. Of course I did, he was the man that brought me here and we had a successful season.
"But I did not say I wanted to go to Liverpool or anywhere else - I am very happy here at Swansea. Not once have I told my agent or the chairman Huw Jenkins that I want to leave here."
Swansea take on Southampton later today in the Premier League.