
Swans are hopeful a deal can be struck for the centre-back in the coming days to make him their first addition of the summer.
Reports initially appeared north of the border, with our colleagues at the Daily Record reporting that a multi-year deal is being discussed for the centre-half, who is believed to have had offers on the table from other Championship clubs and in Major League Soccer.
WalesOnline understands those reports to be accurate, with Vitor Matos now closing in on his signature.
Formalities are being sorted ahead of the move, with the hope it can be rubber-stamped shortly.
The 26-year-old spent last season loan with Motherwell and excelled there.
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He still had 12 months to run on his Parkhead contract but Welsh has agreed to terminate his deal early in order to get a move done.
WalesOnline understands Welsh is being brought in as added defensive cover at the Swansea.com Stadium, with Ben Cabango and Cameron Burgess needing competition and Ricardo Santos' future far from certain, despite still having a year to run on his contract in SA1.
Welsh came through the ranks with the Hoops and enjoyed a loan stint at Morton during the 2019/20 season as he made his way in the game.
He made his debut for the Scottish giants in February 2020 and went on to play a key part in their subsequent campaigns.
Welsh joined Mechelen on loan in January 2025 and spent most of last season at Motherwell, also on loan. He has been capped by Scotland at under-21 level.
Swansea are set for a busy summer in the transfer market, with the club understood to want to strengthen in a number of areas.
Central defence is one of those, while the club would like to bring in depth at left-back to help out first-choice pick Josh Tymon, with wingers on both sides of the attack also near the top of the wishlist.