The outspoken leg-spinner, who said he was "frustrated on many levels at present", praised Fleming as "the best opposition captain we played against" on his website www.shanewarne.com.
"I believe he brings a lot to the table, a calmness, an intelligent understanding of the game and a very good cricket brain. He's a good communicator too as well as a good leader of men."
Warne, 43, who also wants former Test wicketkeeper Rod Marsh as chairman of selectors, said the current Australian set-up was not working as the players gear up for two Ashes series against England over the next year.
In a post entitled "Where is Australian cricket at? Part 1" on his website, Warne said: "The next 12 months is the biggest 12 months of cricket for the Australian cricket team in a long, long time.
"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."
In Twitter comments on Monday, Warne blasted Cricket Australia's policy of rotating players, which has attracted stinging criticism from other greats of the game.
"I think CA really need to look at the people who are making decisions on all facets of cricket in Australia, we r seriously becoming a joke!" Warne said.
"We have the best batsmen / captain in the world in @MClarke23 (Test captain Michael Clarke) - He needs current cricket people to help him out not muppets," he added.
Cricket Australia CEO James Sutherland has told Warne he is happy to discuss Warne's ideas but has expressed disappointment with the manner in which he expressed his concerns, CA said on its website.
Australia, third in the Test and one-day rankings, lost the recent Twenty20 series against Sri Lanka after drawing the one-day series and beating the visitors in the Test series.
Warne was last week fined Aus$5,000 (US$5,250) for a code of behaviour breach in the domestic Big Bash League.
And he apologised earlier this month after a foul-mouthed rant against West Indian all-rounder Marlon Samuels that earned him a ban and a Aus$4,500 fine.
Warne claimed 708 Test wickets in a celebrated career that also courted controversy, including a fine for taking money from a bookmaker. He was sent home from the 2003 World Cup for taking a banned diuretic.
Also on Wednesday, CA said that Australian pace great Dennis Lillee had been appointed to CA's high-performance team as a fast bowling advisor.