"We've looked at a number of keepers who are out of contract this summer and Martyn is one of them," Swans chairman Huw Jenkins told the Western Mail.
"There has been some communication between us and Martyn, but at the moment we don't know what Cardiff are up to.
"There's obviously something wrong because he became Cardiff's first-choice goalkeeper last season and you would've thought they'd have signed him on straight away.
"Kenny (Jackett, Swans boss) has made it clear he'd be happy to go into the new season without signing a new keeper, but we'd be delighted if someone of Martyn's calibre was to fall into our laps.
"It would be a reflection of how the club is moving on."
Margetson has one cap for Wales after coming on as a sub against Canada in May and would be replacing another goalkeeper with just one cap for Wales in Roger Freestone.
Freestone was released 13 years after joining the Swans from Chelsea.
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