Murty will take charge for a second game when the Ibrox side travel to take on Dundee tomorrow but is under no illusion that he is not qualified for the full-time role.
While Celtic manager Brendan Rodgers has warned that prospective candididates may be put off by an apparent lack of communication and unity of purpose at Ibrox, Murty is adamant that big names should “covet” the manager’s job at Rangers.
Murty said: “If it’s not one they [managers] covet then it should be.
“Every occasion I’ve been to Ibrox has been awe-inspiring and I’ve been to some of the best stadiums in the world.
“My brother in law is a Newcastle United fan and he came to an Old Firm game at Ibrox and was absolutely blown away.
“If you don’t covet the Rangers job then have a think about what it is and realise the opportunity that is there to put this club back at the top of Scottish football and I’ve no doubt that is what is going to happen.”
The job opened up when Mark Warburton left – having resigned along with assistant manager Davie Weir and head of recruitment Frank McParland, according to Ibrox chairman Dave King.
The trio deny having resigned but King and the Ibrox board are pressing ahead with a new structure involving a Director Football and may appoint a short-term boss until the end of the season when a full-time manager will be sought.
Murty doesn’t covet the post because of his limited experience of coaching beyond youth and under-20s level
He added: “It would be incredibly arrogant for me with my coaching background to think that I had a chance of being the permanent manager of Rangers. Some of the names that have been mentioned are stellar names and quite rightly because this club deserves a stellar manager.
“I’ll do the best I can until I’m told otherwise. I’m not looking any further than two weeks from now.”
Among those linked with the vacancy so far have been former Rangers and Scotland boss Alex McLeish, ex-Ibrox player Ronald De Boer, former Derby and Nottingham Forest boss Billy Davies and Pako Ayesteran, formerly Valencia manager.