Press Association Sport understands an initial approach was being made to the Irishman who, along with Mark Hughes, are the leading contenders for the vacancy created by Bruce's departure last night.
O'Neill has been out of football since leaving Aston Villa in acrimonious circumstances in August last year, while Hughes parted company with Fulham in June.
Sources close to both men have indicated they are interested in the post and bookmakers have installed the pair at the head of the field, with both having enjoyed favouritism during the last 24 hours in a fluctuating market.
However, it is understood O'Neill - who was being quoted as a 4/11 shot by William Hill on Thursday evening - enjoys the greater support with the people who matter at the Stadium of Light and is currently the preferred choice.
But despite hoping to make a swift appointment, chairman Ellis Short and his predecessor Niall Quinn - who has taken on an international development role since standing down - will not back themselves into a corner.
O'Neill would certainly be a popular choice with the fans, who have repeatedly cited his boyhood fondness for the club as a major factor in attracting him to Wearside, and he has topped the betting at some point whenever a vacancy has existed in recent years.
The fact that he, like Hughes, is currently out of work means there would be no need for lengthy and potentially costly negotiations over compensation, an obstacle which tends to suggest another popular choice with supporters, Everton's David Moyes, would be a non-starter.
Speculation has also thrown up the names of overseas candidates Carlos Queiroz and Ronald Koeman, but a domestic appointment is more likely.
The success of Sunderland's mission to land O'Neill could depend largely on the financial package the club can put together, not only for him and his staff, but for a January reshuffle of a squad which has underachieved this season to date.
Source: PA
Source: PA