The Dutch club claimed a fortnight ago that the Premier League side had expressed interest in the Frenchman and were bracing themselves for a bid.
However, the offer has been rejected by the Eredivisie outfit after the asking price for the 29-year-old was not met.
The Dutch club's general director, Wilko van Schaik, told RTV Utrecht: ''Swansea made us a bid. We rated it as too low.
"We can use the money but that is not to say we give away our players for bargain fees."
Duplan won the supporters' player of the year award last season and is out of contract at the end of the next campaign.
He has appeared just over 30 times for the club, scoring five goals.