Rangers sacked caretaker manager Graeme Murty on Tuesday, clearing the way for Liverpool under-18s coach Steven Gerrard to lead the club.
Murty, installed as the Gers' interim coach in October after the sacking of Pedro Caixinha, wanted the job full-time and had initially been told that he would be able to finish the season in the role.
But Murty's claims were severely dented on Sunday when Rangers lost 5-0 to Celtic at Parkhead, a result that secured the Scottish Premiership title for the Bhoys.
Jimmy Nicholl and Jonatan Johansson will lead the team for their final three games, the club announced.
Earlier, Celtic boss Brendan Rodgers criticised Rangers for speaking with Gerrard about the job as he believed Murty was undermined.
"He's just been thrown to the garbage really and I think it's very, very discourteous," Rodgers told talkSPORT.
"I'm a wee bit reluctant to talk on it too much, purely because Graeme Murty has been put in a job. Last year, he was under-20s coach and everyone was saying 'he's a good guy and he's doing very well.
"The guy went in there and he's done his very, very best in what looks like, from the outside, to be very, very trying and difficult circumstances."
Sources have told ESPN FC that Rangers are confident of appointing Gerrard and have a four-year contract prepared. The Ibrox side would like to announce Gerrard this week with Gary McAllister as his assistant.
"From Stevie's perspective, I know he has always wanted to manage," Rodgers added. "I'm sure one day he will go on and manage Liverpool, but it's all about timing for Stevie.
"If he feels this is the right opportunity then I'm sure he'll look at it, but I haven't spoken to him on it."
Rangers are still in a battle with Aberdeen and Hibernian for second place behind Celtic.