And former Kilmarnock boss Kenny Shiels has told BBC Scotland he would be "very interested" in the role.
Ian Baraclough parted company with the club on Wednesday, a day after the Steelmen had been knocked out of the Scottish League Cup by Greenock Morton.
Former Well captain and current Under-20s coach Stephen Craigan has been put in caretaker charge of the first team.
His first assignment will be at home to Partick Thistle on Saturday.
Shiels, most recently of Thai side BEC Tero Sasana, was considered by Motherwell last year but ultimately missed out as Baraclough was appointed in December.
And, when asked on Radio Scotland's Sportsound about the current vacancy, Shiels said: "I'm very interested because I see it as a good fit for me.
"It's a provincial club and I've had a period now where I've worked in a [Scottish FA] youth academy in Scotland and I can see so much good going on down there with [academy director] Scott Leitch at Motherwell's academy,
"There is a good conveyor belt coming through and I see massive potential at that club, I really do."
The Northern Irishman, who won the Scottish League Cup with Killie in 2012, also indicated he would be willing to work with Motherwell's current coaching staff.
After leaving Killie in 2013, Shiels had a short spell in charge of Morton before his role with the SFA and subsequent move to Thailand. He has also managed several clubs in his homeland.
"One of my greatest skills is the management of the staff and certainly that would be one that I would welcome," he added. "Stephen's a good lad."
Motherwell have received more than 30 applications for the vacant manager's position at Fir Park.