And Sky Sports claims negotiations continue to bring Mawson to West Ham from Wales.
West Ham have been linked with a host of defenders including Armando Izzo and Marlon Santos - as reported by the likes of Sky Sports - and have already signed Issa Diop for £22 million from Toulouse.
But it seems there is still a possibility the former Brentford man could move to the London Stadium if comments from Swansea co-owner Jason Levien are anything to go by.
Levien, who is also managing director of MLS side DC United, was asked about Mawson's potential move to West Ham during the unveiling of Wayne Rooney over in the US and he admitted to Sky Sports the defender could be set to leave.
"Unlcear at this point I would say, there are a couple of different ways that could end up," Levien told Sky Sports News.
"Alfie is a terrific player, he had a fabulous couple of years with us and we value his abilities.
"I think those are better questions to be asked our our chairman than myself because he's on the frontline to those decisions and implementing them," he said when asked if a deal was on the cards with West Ham.
"But certainly we understand the market and I think we understand that there are opportunities for a player like Alfie Mawson because there are going to be clubs that are interested in him."