The Baggies plan to talk to Chris Hughton, who was sacked by Brighton this week, and Lincoln City's Danny Cowley, who has taken the Imps to two promotions in three years, is also on the radar.
The board are keen to make an appointment in the next few weeks, but do not want to rush into one.
Technical director Luke Dowling confirmed: “We’ll start talks next week with a number of head coaches we want to speak to about the role.
"We’ve narrowed it down to four and we won’t manage to speak to all four next week, it will be over the next two weeks.
“We’ll gather our thoughts this end to see who we go back to and probably whittle it down to two off the back of that.
"It could naturally have started the morning after the Villa game but we all wanted to take the rest of this week just to get the emotion out of us.
"It will be an opportunity for us to speak to them about how we see the running of the club. It probably will be a two-week process.
"That doesn’t mean, necessarily, that in two weeks’ time we’ll be announcing a new head coach as it could take a little bit longer than that if they’re in work."
Albion want a head coach who can conjure up more atmospheric nights like Tuesday, when the Baggies nearly overturned a 2-1 deficit against rivals Villa in the play-offs against the odds.
“Walking away from the ground on Tuesday evening, I thought from start to finish it was a night to be proud to work for West Bromwich Albion," said Dowling.
"It showed everyone, not only employees and supporters of our football club, but people who watched it on TV, what we’re about.
“People within football can be very negative but we've received so many positive messages we’ve received about the way the players performed, the hunger they showed, and the atmosphere at the ground.
“It was a proud evening. Obviously, we’ve been knocked out of the play-offs but it’s given us a sense of belief for the future that this is how we want nights to be at Albion.
"We understand every home game won’t be like that but we want to see that more often than not.
“We want our players and head coach to give the supporters the opportunity, through their performance, to get on their feet and sing their hearts out.
"At the end of their week of frustrations at work, or at home, we want them to come and cheer themselves up at The Hawthorns.
"I’ve only been here since September but I’m not sure it’s been the happiest of places over the past few seasons, but that’s something we need to change.
“We will do our upmost behind the scenes to change that. We want to put 11 players out there with a head coach leading them that represent West Bromwich Albion Football Club.
"Everyone mucks in at Albion, from the top down. We want the head coach and players to represent that as well, and we want the fans to see that.
“The fans appreciated Tuesday, it probably reflected West Bromwich as an area, that we work hard for everything that we’ve got. That’s what we want to continue next season."