Heckingbottom has hinted recently that he would be looking to shake up the squad in the summer, and the Mirror suggests that the 21-year-old could be his first signing at his new club.
The Scotland U21 international joined Swansea in 2015 from Bradford City, and has made 16 appearances for the club so far.
He has spent loan spells at Newport County, Bristol Rovers and Barnsley in between. Heckingbottom is keen to bring the Leeds-born striker to Elland Road after bringing him to Oakwell in his last deal as Barnsley manager.
McBurnie has been brilliant for Barnsley since his arrival, and has scored six goals in his last eight games in the Championship.
Pierre-Michel Lasogga has scored 10 goals for Leeds this season but Heckingbottom fears losing him once his loan spell ends in May.
McBurnie is a highly talented young striker with plenty of Championship experience, and will be a superb addition to the side.
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