Mawson, 24, has been widely linked with a move away from the Liberty Stadium since the end of last season.
West Ham United are believed to be interested in the Englishman, while Wolverhampton Wanderers are also said to be in the hunt ahead of the 2018-19 campaign.
Levien has said that Swansea 'value Mawson's abilities', but the American understands that the defender could leave following the Welsh club's relegation to the Championship.
"It's unclear at this point," Sky Sports News quotes Levien as saying. "There are a couple of different ways I would say that could end up. Alfie is a terrific player, he had a fabulous couple of years with us and we value his abilities.
"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."
Mawson, who has two years left to run on his Swansea contract, played in all 38 of his team's Premier League matches last term.