The Scotland international has been hitting the net regularly over the last two seasons, first with Barnsley on loan and then with Swansea last season.
He scored 24 goals in 44 appearances last season as the Swans impressed at times in Graham Potter’s first season in charge.
Steve Cooper is now in charge after a spell working with English youth teams and it’s yet to be made clear how his team will look.
But it’s likely he’ll have to build his Swansea side without McBurnie.
According to The Sun, Sheffield United are on the verge of signing the Scottish striker for £20million.
He’s set to have a medical with the new English Premier League side today so could be paraded as a Blades player over the coming days.
If McBurnie does get his move to the top flight, it’s a big boost for the Scotland national team with another player set to get experience playing at the highest level.