The Sun says he will demand a transfer if Brad Friedel makes a sentimental return to Blackburn.
New Rovers boss Henning Berg has already had one bid to land the veteran United States keeper blocked by Tottenham chief Andre Villas-Boas.
But he will try again for Friedel, 41, in the January transfer window.
If he is successful in bringing Friedel back for a second stint at Ewood Park, Robinson, 33, will be on his way out of the club he joined for £3.5million from Spurs four years ago.
Robbo's agent Rob Segal said: "Paul would be totally happy to stay, he is very happy at Blackburn.
"But, at this stage of his career, he wants to be playing football.
"If Blackburn can sort something out over Brad Friedel, then we shall be on our way."