The prospect could happen because the personal allowance – the level at which income becomes taxable – is stuck at £12,570 at least until 2028.
But the state pension, which pays 12.9 million men and women over the age of 66 up to £11,973 a year, is on track to breach that limit before then because of higher-than-expected growth in wages – especially in the public sector.
Under the triple-lock, the state pension increases by the rate of inflation, annual earnings growth or 2.5 per cent – whichever is the highest.
The Mail on Sunday reported that if average earnings continue to grow at their current rate of 5.2% next year’s state pension will rise above the income tax threshold for the first time since it was introduced more than a century ago.
This will force pensioners who rely entirely on the state pension to pay the basic tax rate of 20% on any amount above the personal allowance limit.
The exact figure will be confirmed later this year.
Shadow Chancellor Sir Mel Stride said: “Labour have shown where their priorities lie. Last winter, they deprived millions of vulnerable pensioners of their winter fuel payments.
“Next year they will start taxing people who rely on the state pension as their only income in retirement.”
He added: “At the election last year the Conservatives promised to protect the state pension from being dragged into tax – Labour chose not to match that commitment.
“They claim to be protecting pensioners through the triple lock, but this stealth tax will erode its value.”