Owen Coyle revealed earlier on Sunday that he had received an enquiry for Davies, although he stressed he does not want to sell the 34-year-old, whose current contract expires at the end of the season.
Sunderland have not gone as far as making a formal offer in any case, but O'Neill has admitted he could firm up his interest before Tuesday's transfer deadline.
"I did make an enquiry and Owen (Coyle) would obviously want to try to keep him," O'Neill said after Sunderland's 1-1 FA Cup fourth round draw against Middlesbrough.
"I may well follow that up tomorrow 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 loan out Davies, but could be persuaded to part with the 34-year-old for around £500,000.
