After taking control of the first team in October when Pedro Caixinha departed, Murty was appointed boss in December until the end of the season.
However, his credentials for landing the job on a long-term basis were questioned following Rangers’ 1-0 defeat by Kilmarnock on Saturday, their seventh Ladbrokes Premiership home loss this season which equalled the club’s worst-ever run in 2014-15.
Smith, 70, who guided the Light Blues to nine titles in a row in the first of two spells at the club, was speaking at Ibrox where he was helping publicise a Legends match on Saturday.
Asked if a decision should be made sooner rather than later bearing in mind the short summer break before the start of next season, he said: “I think it is an important factor for everyone at the club, Graeme Murty as well.
“The lad has been sitting in the job now for quite a while and you’ve got that in the back of your head that results one week (means) you can be the manager of Rangers, and everyone says that is a great thing for him, the next they are saying he is not the man for the job.
“So it is not an easy circumstance for him either. I think he has handled it well.”
If Rangers were to make the change, Smith believes the new man has to provide the basis to get back to former glories.
He said: “They can start again and this time maybe bring in a manager who will bring in the stability that is required and build a good platform for a level of success.”
However, the former Scotland manager knows the task of overcoming or even competing with Celtic will not be an easy one.
He said: “I don’t think anyone is going to come with a massive influx of cash to help the team, like at Manchester City or others.
“So a little bit of patience required from everyone but a steady improvement has to be shown.
“At some stage they have got to find a way to find a level of investment that will help.
“There is no doubt that one of the major things that will help is the settling down of the managerial situation and the next thing is the rise in the level of player that comes into the club and that is still required.
“If that can happen they can get back to a circumstance where, first of all they challenge Celtic and then hopefully, if they can go on from there, get back into a winning position on a more regular basis.”