McBurnie has found first-team opportunities hard to come by at the Liberty Stadium, and could be on his way out of the club with Barnsley being his likely destination.
McBurnie is on the fringes at Swansea and Andre Ayew's imminent return from West Ham will push him further down the pecking order.
But it seems Barnsley have won the race to land the youngster, despite interest from the Scottish Premiership side.
The Scotland U21 worldwide has made three more Premier League appearances this season but an August loan move to Barnsley fell through on Deadline Day.
The 21-year-old hails from Leeds, but is a Scotland Under-21 global and boyhood Rangers fan, and the Glasgow giants have made a move to add them to their squad on deadline day.
The midfielder made the switch to Swansea from his boyhood club Bradford in 2015, but has struggled to nail down a place in the starting line-up.
Sky Sports reporter Keith Downie has claimed on his personal Twitter account that Sunderland had "pipped" the Gers to McBurnie's signature, before he ended up agreeing terms to move to Barnsley.
The Scotland under-21 worldwide had been keenly sought after, with Barnsley also said to be looking to make a move for him, but in the end it seems as though he will join the Black Cats.