This development comes after Vincent Kompany departed the Lancashire outfit to join European giants Bayern Munich last Wednesday.
Craig Bellamy and Mike Jackson will be taking interim care of the role while the Burnley board search for a new head coach.
Pardew is the latest name linked, with other candidates including former Chelsea manager Frank Lampard and West Brom’s Carlos Corberan, as per The Athletic.
As stated by Andy Dillon of The Sun, Burnley are believed to have already made contact with Pardew as they begin their search for Kompany’s successor.
The 62-year-old is believed to be interested in a return to full-time management, having not worked in England in over six years.
Additionally, he is keen on attempting to restore Burnley’s top-flight status following their relegation after accumulating a meagre 24 points.
Recent years have seen Pardew endure spells at CSKA Sofia in Bulgaria as director of football and Aris Thessaloniki in Greece as manager, but this role would likely see him become a head coach.
This modern management structure may be a stark contrast to what Pardew is used to, but his Football League success speaks for itself, having won promotion to the Premier League with West Ham.
If Burnley side with the 62-year-old, then they will hope that they can resurrect his coaching career and secure a first-time return to the Premier League.
Alan Pardew links to Burnley are a real shock
Whilst Pardew hasn’t seen the inside of an English football club in six years, he is synonymous with fans across the United Kingdom. From starting his career at Reading to his last Premier League job at West Brom, he has seen a lot.