Sajid Javid has said patients should be charged for GP appointments and A&E visits, as he called the current model of the NHS "unsustainable".
Writing in an op-ed for The Times, the former health secretary said "extending the contributory principle" should be part of radical reforms to combat growing waiting times.
He also called for a "grown-up, hard-headed conversation" about revamping the health service, noting that "too often the appreciation for the NHS has become a religious fervour and a barrier to reform".
Downing Street said the prime minister is not "currently" considering the proposals.
Labour's shadow health secretary Wes Streeting responded to Mr Javid's comments by saying: "Over my dead body."
"An NHS free at the point of use has been its central equitable principle for 75 years. Patients should never have to worry about the bill," he added.
"It's up to Labour, which founded the NHS, to grip the biggest crisis in its history and make it fit for the future."
Prime Minister Rishi Sunak had previously set out plans to fine patients who missed their GP and hospital appointments £10 as he was campaigning for the Tory leadership.
But he scrapped the idea following widespread criticism by health leaders.
Mr Javid proposed that the NHS should replace making people wait with means-tested fees, while "protecting those on low incomes".
"We should look, on a cross-party basis, at extending the contributory principle," he wrote.
"This conversation will not be easy, but it can help the NHS ration its finite supply more effectively."
The Bromsgrove MP, who will not stand at the next election, highlighted Ireland's "nominal" 75 euro (£66) fees for going to an injury unit without a referral, and £20 fees for GP appointments in Norway and Sweden as possible models.
"Too often the appreciation for the NHS has become a religious fervour and a barrier to reform," he added.
"We need to shake off the constraints of political discourse and start having a grown-up, hard-headed conversation about alternatives."
Mr Javid argued in the piece that "the 75-year-old model of the NHS is unsustainable".
His proposal comes amid increased calls for an overhaul of the NHS, and not just from within the Tory party.
Earlier, Mr Streeting told The Guardian: "Reform is not a Conservative word.
"In recent elections, the left has given a lot of people the impression the answer to everything is to pour more money in. Of course investment is needed in the NHS, but ask any patient about their miserable experiences and it's partly about culture and systems. That's got to change too."
It comes after the PM repeatedly refused over the past week to answer whether he uses the NHS or pays for private healthcare, before revealing he is registered with an NHS GP but has used private healthcare "in the past".
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