Allardyce is the bookies favourite to take over at the club with his odds tumbling from 2/1 last week to 4/5 on many lists this morning.
The Hammers clawed back from 2-0 down and could easily have won as they dominated the second half but couldn’t put the finishing touch to their recovery.
Advocaat flew home to Holland last night on a private jet and an announcement from the club is anticipated in the next 24 hours.
Having been denied a winning farewell, he now looks likely to become the sixth manager to leave Sunderland in seven years.
Asked about his future, Advocaat said: ‘I don’t want to discuss my own future, you will hear one way or the other. Let’s wait and see. “It has nothing to do with this game. Yes. I have made a decision on my future.
“I am still manager today and tomorrow.”