Under the existing system, Richard Sharp said he was concerned those on lower incomes paid the same as richer people for the public service broadcaster.

He said the controversial flat-rate levy could be replaced by a charge linked to broadband bills or council tax.

The government is looking at whether to replace the £159-a-year licence fee with a new funding model after 2027.

The cost is due to start rising again with inflation next April, after a two-year freeze.

Mr Sharp, a Tory donor, quit as BBC chairman earlier this year after a report found he breached rules by failing to disclose the role he played in helping then-prime minister Boris Johnson secure an £800,000 loan.

Questioning the fairness of the licence fee, he told The Daily Telegraph's Chopper's Politics podcast: "I would be in favour of a form of a mandatory payment - currently the licence fee.

"There is one issue which is it's regressive, which may need to be addressed."

Pointing out poorer households paid the same price, he added: "You can look at models around the world, there's a broadband tax, there's a household tax and there's the licence fee. Change is disruptive from moving from one mechanism that works to another."

Labour has previously indicated it would consider means-testing the fee if it gained power.

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Women disproportionately prosecuted

Mr Sharp was also concerned the way the licence fee was enforced by door-stepping inspectors meant women were disproportionately likely to be prosecuted for non-payment.

Failing to pay the licence fee is a crime.

Almost 1,000 people a week - seven out of 10 of whom are women - are prosecuted for evasion.

He said: "The two challenges are obviously it's regressive and also that the collection process can fall harder on women because women often answer the door."

Mr Sharp said both sides of the House of Commons "broadly support the BBC", and that any changes to its funding model should be debated in parliament.

But he warned against decriminalising the licence fee, saying it could lead to more people being brought before the civil courts over non-payment.

He said: "The sanction itself drives behaviour. If you go to civil litigation, you actually can increase the amount of litigation that takes place. So it's not as obvious as you think.

"As a result of people paying the licence fee, you get a common good, which is you get an incredible value for what people are actually paying on a household basis."

In the wake of his own experience as chairman, Mr Sharp also said he would advise someone going for the job to "make sure you and your family know what you're getting into" and warned it made them "a target".

He said: "It's a sufficiently important institution that who ever is the chair is vulnerable."

The issue of freelancers and impartiality at the BBC was also "something that needed to be addressed", he said, after the controversy sparked by Gary Lineker when he compared the government's language used to promote its asylum plans to 1930s Germany.