Sky Sports understand that the bid has been turned down by the Championship outfit, who are keen to retain the services of their number one shotstopper.
The Swans have been keen on landing Camp for a number of weeks but have seen their first two offers for the Northern Ireland international rejected.
Other attempts to land the likes of David Stockdale have also been shunned with two weeks to the big Premier League kick-off remaining.
Whether the club will now make a higher offer is unknown.