The Dutchman, though, has said that he has not accepted the offer yet, stating that he will make a decision by Thursday next week.
Advocaat has said that he will discuss the situation with his family before making his final decision.
The 67-year-old has done a remarkable job at the Stadium of Light since taking charge of the team in mid-March following the dismissal of Gus Poyet.
The Dutchman has worked wonders at Sunderland and has kept them safe in the Premier League.
Sunderland secured their survival in the English top flight with a goalless draw against Arsenal away from home at the Emirates Stadium in North London on Wednesday.