The Sun says Gabbidon looks set to join QPR after being invited on their pre-season tour.
The defender, 31, is a free agent after leaving West Ham this summer.
QPR boss Neil Warnock wants to strengthen his squad ahead of their return to the Premier League. Gabbidon will be offered a deal if he impresses at their Cornish training camp.
Ex-Ipswich keeper Brian Murphy has also been invited on tour.