Robinson is believed to be unsettled at Ewood Park as a result of the club's pursuit of former keeper Brad Friedel from Tottenham.
Blackburn are thought to have lined up a move to bring Friedel back to the club in January in a player/coaching role, with the veteran keeper interested in the switch after losing his No.1 spot to Hugo Lloris.
Should the American return to Blackburn it will raise question marks over Robinson's future, with Rovers thought to be willing to let the former England international leave for free to enable them to bring Friedel in.
The news that Robinson could be allowed to leave in January on a free transfer would come as a major shock to supporters as the 33-year-old has been one of Rovers' stand-out performers this season and has been an ever-present in the Championship.
The likes of Fulham, West Ham and West Brom are thought to be weighing up moves for Robinson as they look to bolster their goalkeeping options when the transfer window reopens.