The Northern Ireland keeper is reportedly keen on making the move back to the Premier League, even if it isn't on the most lucrative of contracts.
Camp has been identified as one of Brendan Rodgers' top goalkeeping targets, but the Swans have so far been unable to agree a fee with Forest.
It has been sugggested that a bid of £1.7m has been submitted, but this doesn't look to be enough to persuade Steve McLaren to part with his top stopper.
But if Camp was to push for the move to go through, as the Mirror suggests, it would make it substantially easier for a deal to be thrashed out.
The Swans are keen to sign a new goalkeeper to challenge Jose Moreira for the number one jersey at the Liberty, but their attempts to land David Stockdale from Fulham were unsuccessful.
Stockdale joined Ipswich on loan yesterday.