O'Neill is primed to be named as Giovanni Trapattoni's replacement next week by the Football Association of Ireland, after both parties took their time to make sure the proposed deal was right following lengthy discussions.
Keane tops O'Neill's wishlist as assistant coach and has been sounded out over his interest in the position, with talks to be held next week, according to The Mirror.
The ex-Manchester United skipper has enjoyed a fractious relationship with the Ireland hierarchy in the past, most notably resulting in him being sent home from the Republic's training camp for the 2002 World Cup by Mick McCarthy.
Both men are former Sunderland managers, although Keane has not worked in a coaching capacity since being sacked by Ipswich Town in 2011, while O'Neill was dismissed as Mackems boss in March.
Keane is due to appear alongside O'Neill as a pundit for ITV Sport on Tuesday night, when Manchester United face Real Sociedad in the Champions League.