Steven Gerrard is set to agree a three-year deal as Rangers manager.
Former Liverpool skipper Gerrard admitted he has held "positive talks" with the Glasgow side and Rangers explained they hoped to release news about Murty's successor "in the near future".
Gerrard, who is in charge of the Anfield Under-18 side, is expected to be confirmed as Rangers' new boss when he returns from Rome where he is working for BT Sport as a pundit for tonight's coverage of Liverpool's Champions League clash with Roma.
"Yes, there is truth in the rumours," said the Reds legend.
"I've held initial talks with Rangers and the plan is to pick them up in a couple of days' time. We'll see.
"There is (interest). I've held positive talks with them. I'm busy now for a couple of days but I will pick it up on Thursday and we'll see if we can progress it."
Ibrox chiefs called time on Murty's reign just 48 hours after Sunday's 5-0 thumping by Celtic and while Gerrard finalises the terms of his first job in management, former Northern Ireland star Jimmy Nicholl has taken caretaker charge of the club until the end of the season alongside Jonatan Johansson.
Murty brought the 61-year-old Nicholl, who is also Northern Ireland boss Michael O'Neill's number two, to the club as assistant manager in January.
Rangers currently sit three points behind second-placed Aberdeen and still have to face Kilmarnock at home before trips to the Dons and Hibernian to end the campaign.
Nicholl, a former Millwall and Raith Rovers boss, has been working as assistant to O'Neill since 2015 but only made his return to day-to-day club duties as Falkirk assistant in October - three years on from resigning as Cowdenbeath boss. He was then brought to Rangers, the club he played for in two separate stints.
Former Under-20s coach Murty was due to remain in charge until the end of the season but was relieved of his duties after meeting with Managing Director Stewart Robertson yesterday morning.
Murty was only meant to be a short-term fix after being called in as caretaker boss following Pedro Caixinha's sacking back in October, but he ended up staying in the post for six months as chairman Dave King and his board dithered over appointing a new long-term successor to the Portuguese.
The club said in a statement: "Rangers are grateful to Graeme, who did not hesitate when asked last October to become interim manager after the departure of Pedro Caixinha and then, at the turn of the year, when he was offered the role as manager.
"Graeme has had to contend with difficult and challenging circumstances but conducted himself in a thoroughly professional manner. He will take time to consider his options, which include returning to his role at the Rangers Academy."
Supporters' group 'Follow Rangers' thanked Murty for his service and expressed regret at the lack of a full-time boss for much of the season.
"While we thank Graeme for his contribution, we would question the wisdom of the decision to leave the club without a full time manager for much of the 2017/18 season," the group said in a statement.
It will now fall on Nicholl and Johansson's shoulders to guide Rangers past Aberdeen and Hibernian through to second spot.
The Parkhead mauling saw Rangers drop three points behind the Dons, with only goal difference keeping them in front of fourth-placed Hibs.
Gers travel to Pittodrie next Tuesday before rounding off their campaign against Ulsterman Neil Lennon's in-form Leith outfit at Easter Road on May 13.
A fourth-place finish might not only see Rangers miss out on a Europa League slot should Motherwell beat Celtic in the Scottish Cup final, but it would see them miss out on a £560,000 cash windfall compared to ending the season as runners-up.
Meanwhile, Kris Commons has warned Gerrard it could cost £70million to sort out Rangers.
Former Celtic ace Commons believes the Kop favourite should be under no illusions about the scale of the task.
The former Parkhead playmaker said: "If I was Steven Gerrard looking at that squad, I'd be thinking this is a £50million, £60million, £70million project. I'm talking transfer fees, wages, agents' fees and a long-term process.
"But when you've got a chairman in Dave King asking for a rapid response and that he is going to provide all the funds needed to sustain and make possible that immediate success, it heaps a massive amount of pressure on Steven Gerrard.
"This is a guy who has been working with 16 and 17 year-old kids for eight months.
"I've worked with (Celtic boss) Brendan Rodgers. If I'd been working in youth team-level football and then someone said to me, 'Listen, I'll give you £60million quid, go spend it, bring in whoever you want and then go up against the potential double-Treble winners and we expect you to win a trophy', I don't think I'd sleep much that night."