Wanderers boss Owen Coyle had earlier revealed the Black Cats had made an enquiry over the 34-year-old, whose current contract expires at the end of the season.
Sunderland are yet to make a formal offer, but O'Neill admitted he could firm up his interest during the remaining two days of the winter transfer window after this afternoon's 1-1 FA Cup fourth round draw with Middlesbrough.
O'Neill said: "I did make an enquiry and Owen would obviously want to try to keep him.
"I may well follow that up tomorrow [Monday] morning."
Sunderland's need is pressing with loan signing Nicklas Bendtner expected to be out of action until the middle of next month with a broken nose.
However, Fraizer Campbell eased their worries to a degree when he scored against the Teessiders on his return to senior action after 17 months on the sidelines following two serious knee injuries.
Bolton are understood to be unwilling to agree a loan deal, but could be persuaded to part with their experienced frontman for around £500,000.