The Sunday Mirror says O'Neill is emerging as the hot favourite to take over at Craven Cottage as pressure mounts on Martin Jol.
Fulham lost 2-1 to Cardiff and home fans turned on Jol at the end.
O'Neill, out of work since he was sacked by Sunderland last season, has an impressive track record at reviving struggling clubs.
Friends in football believe the 61-year-old would relish another Premier League challenge.
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