The 21-year-old striker was brought to Oakwell by Heckingbottom, but the 40-year-old left soon after to become the Leeds head coach.
The Scottish striker has revealed that Heckingbottom rates him highly, and has also outlined the kind of relationship the two have.
McBurnie told Sky Sports about Heckingbottom: ”I really got on well with him and he really rated me as a player.
”To be fair, Heckie rang me the day after he took the job at Leeds, just to explain what his thinking was. I would never hold that against him.
“I understand what football is like. It's a short career and he has his own family and his own reasons for doing that.”
Summer bid for Oliver McBurnie?
McBurnie's comments make it clear that Heckingbottom rate him highly, and perhaps Leeds should make a move for the Scottish youngster in the summer of 2018.
The 21-year-old has started life at Barnsley brilliantly, scoring five goals in 520 minutes of Championship football, according to WhoScored - an average of one goal per 104 minutes.
It would be hard for McBurnie to play regularly for the Swansea first team next season, and perhaps Leeds should use the Heckingbottom link to convince the striker to move - on loan perhaps - to Elland Road in the summer of 2018.