The Sun claims Freddy Shepherd made the offer to O'Neill in Glasgow last Sunday - tabling a four-year deal worth £60,000-a-week.
O'Neill stepped down as Celtic boss in May 2005 to support his wife Geraldine as she battled serious illness.
Meanwhile Swiss newspaper Zisch claim that former Bayern Munich chief Ottmar Hitzfeld is in no rush to hop on the next plane to Tyneside: "The interest and the confidence of the club's supporters is a big honour for me. But I shall not decide anything as to my professional future before summer."