Barnsley confirmed the news yesterday ahead of their game against Rotherham and the Tykes decided to withdraw the defender from their squad.
Mawson, 22, joined Barnsley on a free transfer from Brentford just over a year ago and has impressed in his 63 appearances for the club, scoring an impressive 9 goals from the back.
After Swansea's 2-1 defeat to Leicester yesterday afternoon, manager Francesco Guidolin confirmed that the club were trying to sign a defender, but didn't say who.
He said: "We are working to sign a player - a central defender. This is all I know at the moment because the chairman is working for this situation.
"I'm optimistic [for signings] but I have always said that I'm happy with this group".