High on their list of questions is whether Walter Smith will still be manager next season and whether he will be given money to spend on strengthening his squad for the defence of their crown.
Smith and his backroom staff have been working without contracts since January and the Rangers Supporters' Trust want him secured on a new deal after the 62-year-old guided Rangers to a second successive championship at the weekend.
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Hide AdIt is understood that talks over a potential takeover remain ongoing with London-based property developer Andrew Ellis. And the Ibrox faithful have also urged clarity over the running of the club ahead of the new campaign as the search for a new owner continues.
RST spokesman David Edgar said: "The fans decided to focus on getting behind the team and pushing them over the line to get the trophy. We've done that and now it is time for answers.
"Fans have been asked to stump up season ticket money, without knowing who's going to own the club, who's going to manage the club and who's going to be playing for the club, which is a ridiculous situation.
"I think David Murray gets away with a hell of a lot. Walter Smith's success has deflected some of the fury which could justifiably be shown towards Murray. His mis-management of Rangers has been catastrophic. Rangers' current situation is pathetic and it should never have been allowed to get anywhere near this. The fans are now entitled to ask 'What is happening? Where are we going?' What Walter achieved is a miracle and you can't keep expecting miracles to happen.
"The fans have been very patient this season but we are now coming to the stage where we are in this ludicrous situation where Rangers fans are being asked to pay despite not having a clue what will be going on next season. The club have got to get themselves into a position where they are able to answer some of these questions.
"What the Rangers support want is new investment, the manager secured and the team strengthened so we can defend the title he has done so remarkably well to win."
Rangers chief executive Martin Bain revealed he hopes Smith will make a decision over his future in the coming days and Edgar admits the departure of the veteran manager would be a major blow.
"It would be a massive concern because how do you replace him?" he said. "It's not so simple. Rangers saw it with Paul Le Guen and Celtic saw it with Tony Mowbray. Sometimes it is down-played in Scotland just how difficult it is to win the title here and how difficult it is to build a winning team.
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Hide Ad"This assumption that if you go out and get a guy from a bigger league that he'll automatically know how to do it, I don't think it works like that.
"Rangers have a proven manager, they have a guy who knows how to win titles, who knows the Scottish game, who knows how to deliver. If he was to walk away, it would leave a massive void. I think Smith is now up there just behind Bill Struth as Rangers' greatest manager. If we were to lose him, whoever comes in has a giant pair of shoes to fill."
The RST was behind a proposed supporters' takeover of the club several weeks ago and Edgar says they have not given up on the idea of fan ownership.
He said: "We got really close this season to making it happen and it's very disappointing it didn't. But we are getting closer each time, we are learning the lessons and we are working day and night to try to secure the investment needed to make this a goer. We are not prepared to sit back and wait for a white knight riding in over the horizon. We are going to keep doing it because the one constant about football clubs is the supporters.
"Managers, chairmen, players come and go but we are there for life so we are the ideal people to own the club."
How much Old Firm teams cost
Rangers
Allan McGregor: Youth system
Maurice Edu: 2.6m
David Weir: Free transfer
Sasa Papac: 1m
Lee McCulloch: 2.25m
Steve Davis: 3m
Kevin Thomson: 2m
Kris Boyd: 400,000
Nacho Novo: 450,000
Steven Naismith: 2m
Steven Whittaker: 2m
Kenny Miller: 2m
DaMarcus Beasley: 700,000
Kirk Broadfoot: 1.5m
Madjid Bougherra: 2.5m
Neil Alexander: Free
Steven Smith: Youth system
Kyle Lafferty: 3m
John Fleck: Youth system
Danny Wilson: Youth system
Total paid (20 players) 22.4m
Celtic
Artur Boruc: : 3m (estimated)
Andreas Hinkel: 1.9m
Lee Naylor: 600,000
Scott Brown: 4.5m
Georgios Samaras: 1m
Marc-Antoine Fortune: 3.8m
Mark Wilson 500,000
Shaun Maloney : 1m
Niall McGinn: Youth system
Jos Hooiveld: 1.8m
Marc Crosas: 1.3m
Ki Sung Yueng : 2.4m
Morten Rasmussen: 1m
Pat McCourt: 500,000 (estimated)
Glenn Loovens: 2.5m
Lukasz Zaluska: Free
Thomas Rogne: Free
Zheng Zhi: Free
Josh Thompson: 250,000
Aiden McGeady: Youth system
Darren O'Dea: Youth system
Paul Caddis: Youth system
Paul McGowan: Youth system
TOTAL (23 men) 26m
Plus loan signings: Robbie Keane (estimated 1.3m in wages), Landry Nguemo, Diomansy Kamara, Edson Braafheid.