The Baggies board met yesterday to discuss their options, with Preston North End boss Alex Neil and former Fulham boss Slavisa Jokanovic the two main targets.
However, Preston chairman Peter Ridsdale is keen to cling onto Neil with eight games left this season because his club are currently outside the play-off spots on goal difference only.
Albion are yet to agree a deal with out-of-work Jokanovic, who worked with technical director Luke Dowling at Watford.
There are concerns his methods may take time to bed in and Albion need a short-term fix for the rest of the season.
The different demands of the Championship and the Premier League are also being taken into account.
The Baggies are keen to get their long-term appointment correct for the division they will be in.
Following two wins and two clean sheets, the board believe there is no great urgency to rush into an appointment in the next couple of days.
With so few games left this season, they are now seriously considering appointing an experienced coach on a short-term basis to assist caretaker boss James Shan until the end of the season.
Michael Appleton is under consideration for that role and has worked with Shan in the academy before.
Although he would be open to an approach, he is close friends with Darren Moore, which may give him pause for thought.
There are also other candidates under consideration, and it’s believed former Birmingham City and Derby County boss Gary Rowett would also be open to an approach.
Shan is likely be involved in the first team until the end of the season, regardless of the decision, and he believes he’ll have useful information to pass on to the new boss.
“I was appointed as first-team coach so I’ve worked with the players now for the whole season and some of them for 11 months,” he said.
“I’ve worked with some of the players who have been here a long time for many years when they’ve played for or trained with the under-23s.
“I have a good understanding of the group technically and tactically and where they are physically and mentally.”