Robinson, who has spent the last five years at Ewood Park, has lost his place in the first-team this season to Jake Kean.
At the age of 33, he is eager to find regular football elsewhere and has been linked with West Ham United.
He will not look to force through a move, but Blackburn concede they would allow him to leave on a short-term deal if an enticing offer arrived.
They would be looking for any interested party to help supplement Robinson's wages, with the Championship outfit in the process of trying to cut costs.
Rovers boss Michael Appleton said: "It would have to be the right club for us in terms of what they're prepared to do in terms of salary.
"We've talked but not once has Paul said he doesn't want to play for us."