Mawson has been heavily linked with Watford and West Ham in the January transfer window, while Celtic and Everton are also reportedly interested in the 23-year-old Londoner.
Swansea signed Mawson from Barnsley for £5million in August 2016 and he has two-and-a-half-years left on his contract at the Liberty Stadium.
But Carvalhal insists buying rather than selling is on the agenda of the Premier League's bottom club this month, with the Portuguese saying that chairman Huw Jenkins has given him assurances that Mawson will not be leaving the club.
"When I signed [as manager last month] it was very clear we would try and bring in players to improve the team," he said.
"We will not sell the best players in January, the message is clear.
"I have had guarantees from the chairman, but it depends if someone comes in and gives £50million, £100million, £250million.
"Of course, then it is completely different - to me, (Philippe) Coutinho or Neymar.
"You can never say that it will not happen, but the fundamental idea is not to sell players and try to improve the team."