Reports surfaced last week claiming the Black Cats were lining up a move for Curbishley to help them stave off the threat of relegation.
But Sunderland chairman Niall Quinn played down the speculation on Thursday insisting the board fully support current manager Ricky Sbragia.
When asked if there was any truth in the Sunderland rumours, Curbishley told Sky Sports News: "No truth whatsoever.
Curbishley, who has been out of work since leaving West Ham seven months ago, has ruled out managing outside the top flight saying he wants to return to management in the Premier League
"The last ten years I have had in the Premier League and my average position has been tenth or mid-table or boring mid-table as people call it.
"But I feel that is perhaps where I should be and that is what I will be hoping to get."
Curbishley also rejected the possibility of returning to former club Charlton to help them out of their current struggles.
Charlton could be relegated to League One this weekend if they lose to Blackpool and Curbishley believes the board must take some of the blame for their slump because of the managerial merry go round at The Valley.
"Decision making has perhaps not been as good as it should have been," added Curbishley.
"Two managers in 25 years, one manager in 15 years then suddenly three or four managers in a couple of years and it is very, very difficult as the club was built on stability."