Tomorrow’s quarter-final tie against Hamilton at Ibrox looks likely to be Murty’s final match in charge of the first team, with Mark Warburton’s permanent successor expected to be unveiled next week.
Murty has experienced mixed fortunes in terms of results since being thrust into the spotlight three weeks ago, with two wins and two defeats on his ledger so far.
But the club’s head development coach has consistently impressed with his demeanour off the pitch in suddenly having to deal with being the public face of Rangers.
The former Reading and Scotland defender has certainly done his reputation no harm within the club where his efforts in difficult circumstances have been appreciated by the board of directors, while his contribution on the training ground has earned the respect of the senior players.
It remains to be seen whether Murty will retain a role on the first team backroom staff of the new manager or whether he will simply revert to his job with the under-20 development squad.
Either way, the 42-year-old hopes to emerge from the period with Rangers in a position from which they can build some positive momentum for both the immediate and longer-term future. He said: “I would never presume to offer my thoughts or services to the new manager.
“It is up to him, whatever he wants. If he would like to speak to me, then fine. If not, then I am sure he will have his own ideas. I am perfectly comfortable either way.
“I haven’t even considered it [being part of the first team coaching staff] to be honest. I’m like a swan at the moment – you’re seeing the serene bit with me sitting here with you right now but I’m paddling like you’d never know underneath!
“I’m just cracking on with the bits that I’ve been given responsibility for at the minute, and whatever happens after that, then we’ll have a look at it.
“It’s important for the football club that we put it back in the position where it needs to be. If this game on Saturday goes some way to doing that, in terms of getting into the semi-finals of the Scottish Cup, then fine. But we have to make sure that we, as the people who are responsible for the performance, get that bit right and don’t worry about anything else.”
It was an understandably more upbeat Murty who faced the media yesterday, having overseen a dramatic but deserved 3-2 Premiership win over St Johnstone at Ibrox on Wednesday night.
It was an evening he was able to savour all the more in the company of his wife Karen and nine-year-old daughter Freya afterwards.
“I didn’t get a chance for the glass of wine I’d promised myself because my little girl was at her first game with me in charge and she was hyper,” he smiled. “It was more a case of calming her down than me relaxing.
“It’s been hard to give my wife and daughter the time they need recently, because this job is all consuming. I love my football, but making my wife and my little daughter smile on a daily basis is much more important for my way of thinking. So for them to be there on Wednesday and share that with me was special for us as a family group.
“You have to push yourself, whatever you do in life. Why go into something half-hearted? But as demanding as this job is, you have to find a way to ground yourself and get away from it. It can consume you, so you have to hold onto the things which keep you being the level-headed person you hope you are.”