The Office for National Statistics (ONS) has started a consultation on changes to the calculation of the retail prices index (RPI).
These would make the RPI move more slowly, in step with the consumer prices index (CPI).
Pension experts have warned that any changes would cut pensioners' incomes.
The ONS is independent of the government and says it wants to see if there is any need to make a change.
But in the light of the government's controversial changes in 2011 - which moved the uprating of public sector pensions from RPI to CPI, as well as the uprating of benefits and tax credits - critics may see any move by the ONS as a back-door method for the government to save money.
Darren Philp of the National Association of Pension Funds (NAPF) said any rewiring of the RPI would have "huge implications".
"Pension funds are major investors in government debt and changes to index-linked bonds could have far-reaching impacts on those investments," he said.
"It could also alter the amount by which pensions being paid to former workers are increased each year."
As well as private sector pensions, RPI changes would affect the value of inflation linked savings certificates and index linked bonds, or gilts, issued by the government.
The RPI usually rises faster than the CPI, with an average gap of 0.9 percentage points each year since CPI was first used in 1996.
The gap has been due to a variety of factors:
The overall gap between RPI and CPI is very volatile from month to month and year to year.
In August the gap was 0.4 percentage points, but in recent year has been as wide as 2.3 percentage points, back in August 2007.
The "formula effect" historically has contributed about half of the average gap between the two measures.
But since the start of 2010, when the ONS changed the way it measured movements in the prices of clothes, the formula effect has become the most dominant influence.
The Office for Budget Responsibiity (OBR) has forecast that the overall gap between the two inflation measures will widen in the coming years, to an average of 1.4 percentage points during the rest of this decade.
Linda Whitney, of the actuaries Aon Hewitt, said there was a danger that most people might not realise the importance of this issue.
"Our research has shown that most people do not even understand the concept of inflation, let alone the significance of a change to the way RPI is calculated," she said.
Possible changes
The options the ONS is going to look at are: no change at all; partial changes to the RPI's formula, which would reduce the gap with CPI slightly; or changing the construction of RPI to remove the formula effect altogether, which would shrink the overall gap considerably.
Any change would inevitably ensure that RPI rose more slowly than would otherwise have been the case and make it similar to the CPI.
This would directly depress future increases in private sector pensions.
It would also cut the returns on the £18bn worth of inflation-linked policies which have been sold by National Savings and Investment (NS&I), and also the return on index-linked bonds sold by the government to professional investors.
If there was any potential detriment to gilt holders, whose index-linked holdings are currently worth £349bn, a change would have to be approved by the Bank of England and even the Chancellor of the Exchequer.
Some gilt holders would also be able to demand that their holdings be redeemed immediately if the RPI formula was altered.
Changes to RPI may be seen as just a way to reverse the boost given to the formula effect in 2010, and to rein in its exaggerated influence on the figures.
One group of people which has become keenly aware of the importance of any change from RPI to CPI are 30,000 British Airways pensioners.
Some members of the Airways Pension Scheme (APS) have spent the past year or so campaigning against the decision of their scheme trustees to move from RPI to CPI for pension uprating, in the wake of the public sector changes.
The leader of the aggrieved BA pensioners, Capt Mike Post, said: "Even the cleverest of people can be unaware of the importance of a change, especially when it is compounded over many years in retirement."
The consultation lasts until the end of October, with any changes starting in March next year.
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