Mr Costello, now chair of the Future Fund, was speaking as the central bank holds its first meeting of the year on Tuesday.
Since its last gathering the unemployment rate has dropped to 4.2 per cent, a year earlier than the RBA had been predicting, while inflation is also running well ahead of its expectations.
Financial markets are pricing in the risk of a rise in the cash rate from a record low 0.1 per cent by mid-year, while economists appear to be gravitating to the August board meeting.
Economists, and Mr Costello, expect the RBA meeting to agree to ditch its bond-buying program, otherwise know as quantatitive easing or QE.
Until late last year, the RBA was indicating that a rise in the cash rate would not occur until 2024.
"Plainly that's not tenable," Mr Costello told reporters at a portfolio update for the Future Fund.
"The Reserve Bank has got to start changing its rhetoric and it has got to start preparing for the inevitable. It's got to start preparing the market for a rate rise whether they come in the back end of this year or whether they come next year."
Federal minister Jane Hume played down the impact of a potential rate rise on households, while issuing a reminder that the RBA is an independent body and makes decisions that are separate from government.
"Interest rates have been at an historical low now for a considerable period of time," she told Sky News.
She conceded that the cost of living is high, and there is pressure on household budgets and interest rates will have affect on that.
"The fact that Australians have more money in pockets now, thanks to the Morrison government's economic responses to COVID-19, there are tax cuts, there are more people employed now ... that's something I think that gives us cause for optimism," Senator Hume said.
Labor frontbencher Jason Clare was not so optimistic, saying whoever wins the federal election in a few months time will face higher interest rates.
"That will mean, for a lot of Aussies who stretch themselves to get a mortgage, then it's going to be tougher to pay a mortgage in the future," he told Sky News.
"Of course, that's all going to happen at a time where other things are going up - childcare costs are going up, the cost of petrol is going up. The only thing that's not going up at the moment is wages."
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