The Gillard government has launched a stinging attack on the economic credentials of Peter Costello, deeming the former treasurer is not up to the job of heading up the Future Fund.

Yesterday Labor confirmed David Gonski as the replacement for outgoing chairman David Murray despite reports the overwhelming view of the board of guardians had backed Mr Costello for the job.

Mr Gonski - who recently led the review into the education system - was initially engaged to advise Prime Minister Julia Gillard and Treasurer Wayne Swan to canvass the views of the seven Future Fund guardians - including Mr Costello - about who should be the new chairman.

He duly reported back to the government that the board was in favour of Mr Costello to replace Mr Murray, only to be appointed to the position himself.

Communications Minister Stephen Conroy was the first out of the blocks this morning criticising Mr Costello's record and accusing him of engineering the media reports of the board's views, saying it was ''no surprise to see Peter Costello stamping his feet and leaking stories to newspapers''.

''There are some days when you just know how John Howard felt. 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,'' Senator Conroy said today.

''But I tell you what, I'd rather put my money under the control of David Gonski any day of the week ahead of Peter Costello.''

Senator Conroy's attack was closely followed by Finance Minister Penny Wong who said the government did not believe Mr Costello was the best person for the job - despite the fact Labor had appointed him to the board.

''He has many qualities but we did not believe he is the best person to take up the chairmanship,'' she said. Senator Wong said the government made its decision on ''very sound reasoning'' and had chosen

Mr Gonski because it wanted someone who had ''deep standing in the business community and who had a track record as a business leader''.

Ms Gillard also backed cabinet's appointment of  Mr Gonski while visiting a Canberra school this morning.

''David Gonski is the best person for the job that's why he was selected,'' Ms Gillard said. The Prime Minister said that being the chair of the Future Fund was different from being on the board. ''It requires different competencies,'' she said.

When pressed on what specific competencies Mr Costello lacked - given he had run the federal budget - Ms Gillard deferred to Senator Wong.

''Senator Wong has dealt with these questions today. The obligation of government is to pick the best person for the job and we did.''

Former prime minister and Costello rival, John Howard this morning came out to support his former deputy this morning, arguing his political background worked against him.

''Peter Costello was the best Treasurer this country's ever had,'' Mr Howard said.

''I'm not criticising David Gonski, but the way in which this thing has been handled is just shambolic,'' Mr Howard said, noting that the government had 12 months of warning about the vacancy.

Opposition Leader Tony Abbott said that the Future Fund existed due to Mr Costello and his ability to deliver consistent budget surpluses.

''I can think of no better person than Peter Costello to manage taxpayers' money,'' he told reporters during a visit to a Canberra hospital this morning.

The $73 billion Future Fund was established in 2006 to help the government meet the cost of public sector superannuation liabilities in the future.

Mr Gonski is the chairman of ASX Group, Investec Bank, Coca-Cola Amatil and Ingeus Ltd, a director of Singapore Airlines.

Government Attacks Peter Costello