The changes suggested by the Financial Conduct Authority (FCA) call on firms to take a more proactive approach with struggling customers.
It could mean agreeing repayment plans to clear the debt quicker; or firms reducing, waiving or cancelling interest or charges where a repayment plan is still unaffordable.
Customers who fail to cooperate or who cannot afford the repayment plans would lose the use of their cards.
An FCA study found many firms did not intervene because persistent debtors - defined as those who have paid more in interest and charges than in actual debt repayments over an 18-month period - are often very profitable.
It estimates around 3.3 million people in the UK are in persistent debt, with more than half (1.8 million) remaining so for at least two consecutive periods of 18 months.
The proposals also suggest giving customers greater control over increases to their credit limits by offering choices around how and when increases can be offered and making the process of declining them more straightforward.
Andrew Bailey, FCA chief executive, said the proposed changes would give customers greater control.
"Persistent debt can be very expensive - costing customers on average around £2.50 for every £1 repaid - and can obscure underlying financial problems," he said.
"Because these customers remain profitable, firms have few incentives to intervene.
"We want to change this situation so that firms and customers will deal with outstanding debt more quickly, and avoid persistent debt in the first place."
A consultation has now been launched on the proposals and will run until July.