Steven Gerrard left Rangers on Thursday to become the new manager at Aston Villa, who sacked Dean Smith last weekend.
Rangers were not expecting to lose the 41-year-old in the middle of the season and they have now been forced into looking for a new manager.
Giovanni van Bronckhorst has emerged as a contender to become the new manager, but the club are also reportedly looking at two other names in addition to the Dutchman.
Dalziel stressed that Rangers must not allow the uncertainty to continue for too long and identify the man they want as soon as possible.
He insisted that it is paramount that Rangers make an appointment soon so that the club can move forward.
The former Rangers star said on Clyde 1’s Superscoreboard: “Rangers have got to follow the same sort of pattern as Aston Villa.
“Aston Villa identified their man quickly, got over the line, got him in and now he is starting to work for them.
“I think Rangers can’t let this fester.
“Probably the whole backroom staff will go as well so we don’t know who will take training.
“I think Rangers have got a massive job in identifying the guy who is going take them forward, get him in the building and get him working right way.”
Rangers will want to get a new man in ahead of their Scottish League Cup semi-final against Hibernian next weekend.
