Allardyce is understood to be on the club’s managerial shortlist in the wake of Advocaat’s weekend resignation.
Former Newcastle United manager Allardyce watched Sunderland’s 2-2 home against West Ham United on Saturday while in Ireland working for broadcaster Setanta.
And the 60-year-old – who had spells at Sunderland as a player and coach earlier in his career – was left in no doubt that the biggest issue is a defence which has leaked 18 goals in eight games.
The timing, however, could be problematic should Sunderland move for Allardyce, whose autobiography is published this month.
Allardyce is due to return to England from Spain later this month for a tour to promote his book, which is entitled ‘Big Sam: My Autobiography’.
Allardyce has been out of work since the summer, when he left West Ham United.