The Republic of Ireland international is available as a free agent after departing Villa Park.
QPR are in the market for an experienced centre-half, having offloaded Chris Samba back to Anzhi Makhachkala.
Dunne would fit the bill, as Harry Redknapp prepares his side for life in the Championship.
No deal has been agreed as yet, but QPR chief executive Phil Beard admits there is a desire on their part to bring the 33-year-old on board.
He said in the Fulham Chronicle: "He's not signed yet but he's a player that Harry would like to bring to the club.
"We're looking at a number of players. The main thing is that they want to play for the club and are ready for the Championship, which is very different to the Premier League."