The Light Blues’ Under-20s coach has been put in charge of the first team following former manager Mark Warburton’s surprise exit.
He will again take on the dugout duties when Gers travel north to Dundee for Sunday’s crucial Ladbrokes Premiership clash.
And while the Ibrox board examine their list of potential replacements for Warburton, managing director Stewart Robertson has told Murty he will be in charge for the “foreseeable future”.
That has raised the prospect that the former Reading defender could still be in the post when Rangers travel across Glasgow to face Brendan Rodgers’ Celtic on March 12.
Given that Warburton’s side were smashed 5-1 on their last trip to Parkhead back in September, Murty can be forgiven for admitting to a sense of intimidation.
Asked if he would be daunted by that challenge, the 42-year-old said: “Absolutely. You look at the history behind the clubs, you look at the way they are playing at the moment then you would be daunted.
“But I always had the feeling when you go to a big stadium and you are the underdog, there was no better feeling than walking out with a good result.
“However, I think it would be incredibly arrogant and presumptuous of me to even look that far forward.
“I’m just cracking on with what I’m doing, then we’ll see what happens after the game.”