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Warne, who earlier this week said on Twitter that Cricket Australia's (CA's) selection policy had become a joke, has also called for a new-look selection panel.
The champion legspinner says Arthur, Andy Bichel and chairman of selectors John Inverarity should be replaced by Warne's ex-teammates Damien Martyn, Mark Waugh and Glenn McGrath.
Warne says the coach shouldn't be a selector, but the skipper should be. Which means captain Michael Clarke would form part of a five-man panel including current selector Rod Marsh in Warne's world.
Marsh would be promoted to chairman of selectors.
Warne, 43, also wants his former test skipper Mark Taylor to take over as CA's chief executive of cricket.
"As an emotional, passionate and Australian cricket team supporter (and player) for the best part of 20 years (a proud one too) I, like many others am frustrated on many levels at present," Warne said on shanewarne.com.
"If we do nothing now, we will be where we were 30 years ago. There needs to be urgent action and a new strategy/plan put in place.
"The current set up is not working, as the results are showing!"
Australia are ranked third in tests and one-day internationals and seventh in Twenty20 cricket.
Warne has made the bizarre claim that the same 11 should play in all three formats.
"You get to know the person, too much chopping and changing leads to insecurity, players then start to look out for themselves and over their shoulder, this breeds selfishness," Warne said.
"It's also why rotation and resting players will never work.
"We have the best batsman/captain in world cricket at the moment in Michael Clarke and the spine of a good team with (David) Warner, (Shane) Watson, (Matthew) Wade, (Peter) Siddle and (Nathan) Lyon. The rest of the spots are up for grabs in my opinion."
Warne described Fleming as the best opposing captain he encountered in his playing career.
Warne's close mate Darren Lehmann, the Queensland coach, would be national assistant coach.
Ex-players Mike Hussey and Michael Bevan would be batting coaches with Merv Hughes and Bruce Reid in charge of bowling.
Warne also wants his mate and former test skipper Ian Chappell as a consultant to the team.
"All the above people are cricket people, not rugby, tennis or from any other sporting code," Warne said, in a clear reference to Australia's high-performance chief Pat Howard who is a former Wallabies rugby international.
"It's time to go back to basics. Too many people are justifying their existence.
"If the following people (listed above) were to fill these roles, then Australian cricket would be in good hands and a great chance of getting back to No.1."
Warne plans to discuss his ideas with CA boss James Sutherland in the next few days.
Warne later attempted to clarify that he wasn't suggesting the same team should be selected across all three forms of the game.
"Pick your best team in all forms of the game at all times, not the same for all forms - no rotating or resting, but your best," he tweeted.