Vorm reportedly told Dutch magazine Voetbal International that it would be "special" to again link-up with Rodgers, the man who brought him to the Liberty Stadium from FC Utrecht in the summer of 2011.
The 29-year-old Dutch international, whose contract in south Wales runs until 2016, has been linked with a move to Anfield, as well as Arsenal and Barcelona, but he claimed his comments on Rodgers had been "lost in translation".
He told the club's official website www.swanseacity.net: "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."
Earlier this week Vorm and Jenkins had to deny talks had already started over a move to Barcelona, after the keeper and his family were spotted in the Catalan city.
"The Barcelona story was a shock to me," added Vorm. "It's quite funny when I think about it, because I had a couple of days free so I wanted to fly somewhere close and sunny, so my family went to Barcelona.
"I had a great time with my wife and my two kids. We went to Barcelona Zoo, but I can tell you we were not buying souvenirs at the Camp Nou."
And he made it clear he fully intends to be part of Swansea's foray into European competition next season.
"This season has been incredible for us," added Vorm. "We are doing so well in the league and, of course, we won the Capital One Cup which means we are playing in Europe next season.
"I've played European football before and it will be great for everyone at this club - the players, staff, directors, supporters and also the city of Swansea.
"Everyone is looking forward to being a part of that adventure - myself included - but first of all we must ensure that we finish this season strongly."
Swansea will look to end a run of four games without a win when they face Southampton in Saturday.