McBurnie has rejected a new contract at Swansea City, as he wants to move back to Yorkshire.
Leeds have reportedly beaten off competition from a host of clubs, including Derby County, Sheffield Wednesday and Glasgow Rangers with McBurnie now favouring a move to Elland Road over any other option.
The potential signing is sure to capture the imagination of Leeds fans, as the 21-year-old has been in brilliant form at Barnsley this term.
McBurnie has hit eight goals in 13 appearances for the Tykes, after he joined them on loan from Swansea in January.
Swansea had wanted to keep McBurnie, but the prospect of moving to Leeds has reportedly turned his head, and he will reject their contract offer, which means he will have just one year left until his deal expires in 2019.
Leeds desperately need a goalscorer, as they have found their striking options weak this term, and McBurnie could have the potential to fill that void in their squad next term.