The Black Cats, who had earlier made an enquiry about the 34-year-old, firmed up their interest on Monday morning, but were met with a flat refusal.
O'Neill said: "We have have made an offer to Bolton for him, and that has been rejected at the moment. We will see where we stand later on today (Monday)."
Bolton boss Owen Coyle had earlier insisted he wanted to keep his captain, but admitted it could depend on the player.
O'Neill added: "We would have to organise something with Bolton first of all and at the moment, we seem to be apart in those aspects.
"But perhaps later on today, I might have a better idea."
O'Neill also confirmed that midfielder Craig Gardner will not be allowed to leave the club ahead of Tuesday's transfer deadline.
Source: PA
Source: PA