كتب : Hatem Maher
Reports suggested the Dutchman would leave Real following the arrival of Kaka and Cristiano Ronaldo from AC Milan and Manchester United respectively.
Allardyce, who succeeded in signing Nicolas Anelka when he was in charge of Bolton Wanderers in 2006, believes he can bring former United striker Van Nistelrooy back to the Premier League.
"Who'd have thought Bolton would get Anelka? Nobody," he was quoted as saying by BBC Sport.
"It would be a major coup if I could pull it off."
Blackburn eye a new striker after Matt Derbyshire and Roque Santa Cruz left the club.
Van Nistelrooy, a prolific goalscorer, enjoyed a highly-successful three-year spell with Real but was plagued by injuries last season.
Allardyce is concerned that the 32-year-old's salary demands might hinder any talks.
"The sort of salary he would be on at Real Madrid may be beyond us," he said.
"But maybe he wants to come and play in England again and take less of a salary - then we'd be interested."