Murty, 43, has stepped in as caretaker manager at Ibrox for the second time in his short career in coaching, after the Gers hierarchy decided to sack manager Pedro Caixinha last month.
Portuguese manager Caixinha left Rangers in fourth place in the Scottish Premiership behind Celtic, Aberdeen and Hibernian, after a disappointing 1-1 draw against Kilmarnock.
Aberdeen boss Derek McInnes remains favourite to take over at the Scottish giants after turning out as a midfielder for the Gers during his playing days, but Murty's two wins from two also sees him in contention.
The former Reading defender, who was head of youth development at Auchenhowie before being installed as caretaker manager, stated that many have asked him whether he wants to replace Caixinha permanently.
“You think about the people who have sat in the seat I’m currently in, and it’s wild," Murty said.
“It is still very, very special to me. I’ve enjoyed it. What I’d like to do is concentrate on doing the job and not worrying about what might happen in the future.
“I’ve had lots of questions - ‘Do you want it?’ ‘Do you think you should have it?’ – but I just want to crack on with it. The reason I got into coaching is to help players get better and perform. If I’m doing that, you will eventually get to the level you’re supposed to be at.”
Murty is set to take charge of his third game as Rangers interim manager on Saturday, as the Light Blues play host to Hamilton with a third three points in his sights.
An eighth league win of the season for Rangers could see them climb to second in the Scottish Premiership table, if Hibernian drop points to St. Johnstone and Aberdeen lose to Motherwell on Saturday.