A club spokesman told BBC Sport: "We've had no approach - we're treating it just as rumours."
While his agent Mark Curtis confirmed, "Sam won't be going to Sunderland."
Niall Quinn told the Sunderland Echo earlier in the week: "The selection of the next Sunderland manager remains a work in progress, but the reality is that there are three or four names that are in the frame at the moment and that are being considered."
It was understood that 51-year-old, Allardyce was a genuine potential target for the ambitious Irishman.
Meanwhile, Fulham are set to clinch the signing of Bolton target and Lyon attacker Sidney Govou.
The French champions are willing to sell as they want to buy Nicolas Anelka from Fenerbahce and Fulham are set to close a £3.5 million deal for the winger.