The Dutch stopper has been in great form for his side this season, with the Liberty Stadium becoming a fortress for the Welsh club with six clean sheets from 11 games at home.
Vorm in particular has played a crucial role in the team's fine start to their maiden Premier League campaign, including a penalty save as Swansea drew with Wigan at the start of the season, with the 28-year-old's performances attracting the interest of a number of top sides.
"A number of clubs have approached us about [Michel] Vorm," Van Zweden told Voetbal International.
"Manchester United have called, while Chelsea have made an approach as well. Tottenham Hotspur have also told us that they're interested. Vorm's departure would be a nightmare for us though."
Vorm joined the Swans from Dutch side Utrecht in August for a fee of £1.5 million, and he has quickly become a key member of Brendan Rodgers' side.
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