The Man City legend has been heavily linked with the vacant managerial position at Turf Moor following their relegation from the Premier League.
Current caretaker boss Mike Jackson is also being considered for the job, but speculation of Kompany's potential arrival increased in recent days when the former City defender left his position as Anderlecht boss.
Should the 36-year-old be appointed at the Championship side, he is interested in raiding his former club to bring in Harwood-Bellis on loan, according to The Sun.
The 20-year-old played under Kompany for six months in Belgium last season, before becoming unsettled and returning to England to join Championship side Stoke City on loan for the second half of the 2021-22 campaign.
Harwood-Bellis made 22 league appearances for Michael O'Neill's side as they finished 14th in the second tier, before returning to parent club Man City this summer.
The central defender has featured just eight times for Pep Guardiola's first team so far, all of which have arrived in cup competitions, but should he move to Burnley, he is likely to be a replacement for James Tarkowski, who is set to leave Turf Moor upon the expiration of his contract in June.