Reports had claimed that O'Neill had offered to quit his post as Sunderland boss following Saturday's 4-2 home defeat by high-flying West Bromwich Albion.
However, the Black Cats have dismissed the speculation and have confirmed that the Northern Irishman remains in charge on Wearside.
O'Neill is approaching his first anniversary as Black Cats boss after signing a three-year contract to replace Steve Bruce at the helm last December.
He enjoyed an immediate impact in guiding Sunderland away from the relegation zone, but has seen his team win just two of their last 20 Premier League games.
The Black Cats were also knocked out of the Capital One Cup at home by local rivals Middlesbrough last month and have won just once in the league in front of their own supporters this season.
Speaking after the loss against West Brom, which saw Sunderland score twice in a game at home for the first time in the Premier League this term, O'Neill was staying upbeat.
He said: "I think there's a lot to take out of the match, a lot to take out of it.
"We have been beaten, but we look as if we can maybe get a goal again now, which is very encouraging.
"We have a big game on Tuesday night against QPR and we will try to get ourselves prepared for that."