The 21-year-old, who was beaten to death, was found in a barn in Oram, County Monaghan, in October 2007.
Searches of a farm near Castleblayney, on the border between Armagh and Monaghan, began on Thursday at about 09:00 local time.
A man in his 50s, who was arrested that morning, remains in custody.
The BBC understands that specialist ground radar equipment was used to search the area and showed up a large amount of buried items, initially thought to include a van used by the gang who killed Mr Quinn.
A digger was brought in to excavate the items, which were found to be illegal waste, including large household objects.
GardaÃ­ will now sift through the waste to see if it contains anything which could help them with their investigation.
Searches of the area are continuing.
GardaÃ­ (Irish police) investigating the murder of County Armagh man, Paul Quinn, have unearthed a large quantity of illegal waste.