Green has put in a series of erratic displays for Rangers so far this season, and he made a costly error in their latest match against Hull City.
QPR had looked to have been heading towards a draw against the Tigers, before Green failed to clear a cross in the final minute - and allowed Hull to take all three points.
Jimmy Floyd Hasselbaink is now keen to offload the former England international, with Alex Smithies set to get a run of games.
Smithies joined QPR in the summer transfer window from Huddersfield Town, but he has been kept in reserve so far.
Rangers know that by allowing Green to leave they would seriously be reducing their wage bill, which is high on Hasselbaink’s list of priorities.
The R’s are said to be keen to offload a number of first team players - as they plan for another season in the Championship, after their poor start to this campaign.