Tottenham Hotspur are rumoured to be interested in the 23-year-old, who established himself as a key member of Swansea's survival push during the second half of last season.
Mawson admitted that it is "nice" to be linked with a club like Spurs, but stressed that his focus remains fully on the Swans as he prepares for his second campaign at the Liberty Stadium.
"I'm very grounded and very level-headed when it comes to that. It's all speculation. It's nice to hear, but I'm a Swansea player and I'm more than happy here," he is quoted as saying by BBC Sport.
"I love it here. I want to kick on and do great things at this club. There's always talk and there's loads of speculation, but I'm happy to be here under the gaffer. So it's onwards and upwards at this club."
Mawson made 27 Premier League appearances for Swansea last season, scoring four goals.