Denial Costello in running for fund chairman

Finance Minister Mathias Cormann has attempted to hose down suggestions former treasurer Peter Costello is being lined up as the next chairman of the Future Fund, declaring there is "no vacancy" for the $92 billion investment fund.

However, in a fiery Senate estimates hearing, Senator Cormann declined to clearly answer whether he had spoken with Mr Costello regarding the role, describing the question as "hypothetical".

The role is held by businessman David Gonski, who was initially tasked to find a replacement for founding chairman David Murray. Mr Costello established the Future Fund in 2006 and now serves on its board.

Questioned by Labor senator Penny Wong whether he had spoken with Mr Costello about chairing the fund, Senator Cormann said Mr Costello was among the people with whom he met regularly.

"But as I've pointed out before, there is no vacancy," Senator Cormann said.

"I completely reject your assertion. This is completely a hypothetical question and you know it."

The fund was established with $60.5 billion in government contributions to help pay for the unfunded superannuation liabilities of public servants. One of Australia's biggest investors, it has a mandate to return inflation plus 4.5 to 5.5 per cent a year over 10 years.

The hearing was told that the government had not injected money into the fund since 2007, and the gap between the fund's liabilities and assets would continue to grow, although no firm amounts were provided.

The outgoing managing director Mark Burgess told senators there was no date for his departure yet as a replacement had not been found.

The Melbourne-based fund recently announced it had returned 8.2 per cent a year over five years - exceeding its benchmark - and 9.7 per cent a year over the past three years.

The fund confirmed it had sold all of its tobacco investments.