Dutch-based director van Zweden had claimed Manchester United and Chelsea had contacted the Swans about Vorm, who has been one of the stand-out performers of the Premier League season.
But a Swansea spokesman said: "We have not received any enquiries about Michel Vorm."
Holland international Vorm, 28, joined the promoted Swans from FC Utrecht for around £1.5million in August.
Having kept nine clean sheets in 21 games for his new club, he would doubtless command a much larger fee were he to be sold.
But Swansea are desperate to keep hold of one of their prize assets.
Van Zweden told VI Radio: "Clubs have enquired about Vorm.
"Manchester United have asked, in addition Chelsea and, for that matter, Newcastle United. Tottenham Hotspur have cautiously announced they are interested.
"It would be a nightmare for us if he left."
The same would arguably be true were Swansea to lose Scott Sinclair and Joe Allen, both of whom have been linked with a move to Liverpool.