Former treasurer Peter Costello says the international reputation of the $73 billion Future Fund has been damaged in the "shemozzle" over appointing the chair of its board of guardians.

Speaking exclusively to ABC1's 7.30 on Thursday night, Mr Costello lashed out at the process used to appoint Sydney businessman David Gonski to the plum job; for the lengthy delay and because Mr Gonski had been engaged by the Government to recommend a replacement.

The attack comes after it emerged that Federal Cabinet ignored the advice of the Future Fund board in appointing Mr Gonski ahead of Mr Costello, a current board member and the man who set up the fund in 2006.

Mr Costello denied he was moved to attack the decision because he had missed out on the job.

Mr Gonski is chair of the Australian Stock Exchange and considered an eminently qualified chair.

"I have no problem with Mr Gonski, but I ask you this question: If the Government wanted Mr Gonski, why didn't they appoint him 12 months ago?" Mr Costello said.

"And, secondly, why did they ask him to get the confidence of the board and then ignore his recommendation, and thirdly, having got the confidence of the board, don't you think he should have ruled himself out as a candidate?"

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Mr Costello said the Government had four years to find a replacement for founding chairman David Murray and it had extended his tenure by a year in order to buy more time in the hunt for a successor.

"I think the process has been a shemozzle," he said.

"The Government should have appointed somebody 12 months ago on to the board. Given them time to adjust, it would have been ideal as a chairman.

"I think the process under which the Government commissioned a report and leaked it, and leaked it to a selected journalist has created problems for the governance of the fund, and I'm interested in the fund and its international reputation - that's what I want to see protected throughout all of this."

Although Mr Costello was at pains to avoid direct criticism of Mr Gonski, he did question whether Mr Gonski should have accepted the role.

"Mr Gonski, having taken the role of being the person to get the confidence of each individual board member and report back to the Government, I would have thought disqualified him from having his own name put forward and I think that would have been good corporate practice," he said.

The Rudd government appointed Mr Costello to the Future Fund board, but the current Government says he is not the best person for the role of chairman.

'Proven track record'

Finance Minister Penny Wong insists the Government made its decision to appoint Mr Gonski "on very sound reasoning".

"We wanted someone who had a deep standing in the business community, had a proven track record as a leader, someone who had undertaken such important roles as chairing listed companies," she said.

"Mr Gonski has those attributes."

But Communications Minister Stephen Conroy attacked Mr Costello.

"I'd rather put my money under the control of David Gonski any day of the week ahead of Peter Costello," he told Nine's Today program.

"Peter Costello seems to have a sense of entitlement that he should have been the prime minister, so he used to stamp his feet behind John Howard and now he's doing it again."

Mr Costello labelled Senator Conroy's intervention "foolish and juvenile".

"There are certain things I'll cop in public life, but I won't cop that," he said.

"I'd remind Stephen Conroy of this: If I hadn't paid off Australia's debt and accumulated $60 billion in surpluses there would be no Future Fund.

"This Future Fund invests the surpluses that I delivered as treasurer. And for a man like Mr Conroy, whose last outing was set-top boxes and the NBN, to be talking about financial accountability is a bit rich."

The retiring Future Fund chair, Mr Murray, described his successor as a "good appointment" and "a person of stature", but would not be drawn on whether Mr Gonski was the best man for the job.

But former prime minister John Howard also described the appointment process as "shambolic".

"I'm not criticising David Gonksi. He's a man of ability and he has a good reputation in the business community, but the way in which this thing has been handled is just shambolic," he said.

"Everybody knew a year ago that David Murray was standing down, and they even managed to mess [up] something as simple as that.

"Clearly his [Mr Costello's] political background would have worked against him, there's no doubt about that."