The Black Cats boss has denied making contact with Celtic over a move for their in-demand defender, who recently helped Nigeria to victory in the Africa Cup of Nations
The Nigeria international has quickly cemented his status as a key man for the Bhoys since arriving from Israeli side Ashod for a fee of £1.5 million over the summer.
The 24-year-old’s performances are believed to have drawn interest from a number of Premier League clubs, but O’Neill has denied discussing Ambrose's future with Celtic coach Neil Lennon.
"It's been news to me. I've not spoken to Neil Lennon about Ambrose," O'Neill told the Sunderland Echo.
The defender was at fault for two goals and missed a glorious chance at the other end as the Scottish outfit succumbed to a 3-0 defeat at the hands of Juventus last week.
But Lennon has underlined his faith in the player, insisting he simply had an off night against the Italian side.
"I've got a lot of time for him. I've got a lot of faith in him," Lennon told BBC Radio Scotland.
"He just had a bad night [against Juventus]. He's a terrific player and he's got a lot of suitors out there already but he wants to play here.”