The Daily Mail says the 61-year-old held lengthy talks with co-chairman Steve Parish on Sunday.
O'Neill has been out of work since leaving Sunderland in March and has been looking for a route back into management.
He is known to be a front-runner for the vacant Republic of Ireland job following Giovanni Trapattoni's departure in September and is understood to have met with FAI chiefs last week.
But the former Aston Villa boss could be tempted by another crack at the Premier League at Selhurst Park.
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