Dunne is a free agent after being released by Villa earlier this summer following an injury-ravaged season last term.
The Republic of Ireland international failed to play a single game last season due to a serious Achilles injury, but he proved his fitness by featuring for the Republic in a friendly against Georgia in June.
Doncaster Rovers have been weighing up a move for the 33-year-old, but QPR are hopeful of luring the centre-half to Loftus Road, Sky Sports understands.
Rangers boss Harry Redknapp is thought to be a big fan of Dunne and sees him as an ideal replacement for Chris Samba following his return to Anzhi.
Dunne is keen to kick-start his career again and Redknapp sees him as an ideal leader to help his side's bid to win promotion back to the Premier League.