O'Driscoll was appointed manager yesterday on a twelve-month rolling contract, is said to admire O'Kelly as a coach and tactician.
Should The Robins enter an offer to him Walsall would be eligible for a small amount of compensation.
If O'Kelly were to depart, it would be the second time the 56-year-old former striker has left the club, following his arrival in November 2011, Richard left to take up the managers job at Hereford United in March 2012, during their ultimately futile battle against relegation to the Blue Square Bet Premier League.
O'Kelly returned to The Saddlers in June of last year and is seen as a major catalyst for the clubs good form.