Vitor Pereira is Everton's first-choice to replace Marco Silva.
The Daily Mail says Everton's chiefs decided on Pereira after speaking following Saturday's win over Chelsea.
The win has given Everton a chance to take their time with appointing their next manager.
They have decided on Pereira, who is currently in charge of Shanghai SIPG.
The Chinese do not want to lose Pereira and will try their best to keep him.