Caretaker manager James Shan is expected to remain in charge at West Brom for Saturday's trip to Brentford.
Shan, 40, stepped in following the sacking of Darren Moore last Saturday.
He steered the Baggies to a 3-0 win over Swansea on Wednesday, after which he said he was unsure whether he would still be at the helm this weekend.
It is understood the West Brom hierarchy want more time to decide the way forward for the last eight games after March's international break.
West Brom chief executive Mark Jenkins flew back from China on Tuesday after talks with owner Guochuan Lai.
But finding a replacement for Moore has taken longer than initially anticipated.
As yet, there has been no agreement with former Watford and Fulham boss Slavisa Jokanovic, while David Wagner has told the Baggies he is not interested in returning to the game until the summer following his exit from Huddersfield.
Preston boss Alex Neil has been mentioned as one possible option, but BBC Sport understands the Lancashire club would not entertain an approach for their manager given the late stage of the season and the club's present position, two points off a play-off place.
West Brom are fourth in the Championship, nine points clear of seventh-placed Bristol City and nine behind second-placed Leeds.