Bordeaux chairman Jean-Louis Triaud would like Marouane Chamakh's future to be sorted out by the end of the week.
The Moroccan forward has made it clear that he wants to leave the French champions and has been linked with a move to the Premier League.
Arsenal had been tipped to bring him in but Bordeaux rejected their initial offer and Arsene Wenger does not plan to return with an improved bid.
Sunderland were the other club to make no secret of their interest but Bordeaux boss Laurent Blanc only wants Chamakh to join 'a big club'.
Fresh reports in the French press suggest Blackburn have now entered the chase for the 25-year-old's signature.
Triaud is keen for the matter to be resolved quickly as Bordeaux prepare for their opening game of the Ligue 1 season against Lens.
"I would like everything to be sorted out this week or as soon as possible," Triaud told L'Equipe.
Chamakh has returned to training following illness but is not expected to figure in the home clash with Lens on Sunday.