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.