International cricket bosses have issued a veiled threat to Zimbabwe to sort out it's internal strife or risk having Test status suspended.
Mani and Speed believe Zimbabwe Cricket must solve its own problems
ICC chiefs proposed Test suspension in May 2004 after a player strike.
And they said in a statement: "A similar move by the ICC Board cannot be ruled out in the future.
"While members have the freedom to manage their own sovereign affairs, they do not have the right to risk the integrity of the international game."
In a joint statement to the CricInfo website ICC president Ehsan Mani and chief executive Malcolm Speed said the point had been made clear to all parties in this dispute during discussions in recent weeks.
Zimbabwe Cricket chairman Peter Chingoka and managing director Ozias Bvute were recently questioned by police as part of a fraud investigation.
And Tatenda Taibu quit as national team captain in protest at the way the game is being run.
However, Mani and Speed believe direct intervention would do little to resolve "a complex issue".
"The idea that the ICC can simply walk in and 'take over' one of our members is quite simply a nonsense," they said.
Taibu is currently playing club cricket in Bangladesh
"The ICC is well aware of the arguments against its stance and respects the rights of its stakeholders to take and express other opinions on the best way to resolve these difficult issues affecting Zimbabwe Cricket.
"What is more difficult to respect are the attempts by some people to link issues that are not joined, to use rhetoric ahead of reason, and to advance extreme positions at the expense of striking a balanced view."
The pair were responding to criticism from the Federation of International Cricketers' Associations, who claim the ICC's handling of the issue has "disillusioned and disappointed the majority of players around the world".
Zimbabwe's problems off the field have been reflected by a decline in performance on it.
The national team have lost 21 of their last 25 Tests, winning only one, and been beaten in all but two of their last 29 one-day internationals.
Taibu's resignation, the retirement of experienced players like former skippers Heath Streak and Stuart Carlisle and the departure of Sean Ervine to continue his career in England and Australia has left the team short on quality.
And a tour to New Zealand scheduled for this month had to be cancelled after the government refused to grant visas to the Zimbabwe players in protest at the policies being pursued by national president Robert Mugabe.
Taibu has said he will return if Chingoka and Bvute are removed from their positions.