When the Parti Quebecois launched the widely acclaimed program in the late 1990s, parents paid $5 a day to send their children to daycare centres that receive government money.
Since then, the fee has risen to $7.30.
Montreal Le Devoir reported Wednesday that amount will climb to between $8 and $20, beginning next April 1.
The newspaper said the new fees will be as follows:
— $8 to $12 for families with a net income of between $75,000 and $100,000.
— $12 to $15 for those earning between $100,000 and $150,000.
— And $15 to $20 for those with a net income ranging from $150,000 to $200,000.
Couillard suggested a sliding-scale system based on family income is fair.
"We want to maintain the program and we want it to reflect the revenue structure in Quebec," he told the national assembly.
The premier said such a system is fairer than one proposed by the previous PQ government that would have seen the daily fee climb by $2 over two years for all parents whose children attend daycare.
"Low-income families, middle-class families with modest incomes, everybody would have been affected by that," said Couillard.
The PQ, meanwhile, accused the Liberals of breaking a promise from the election campaign to limit any hike to the rate of inflation.
Interim leader Stephane Bedard described the sliding-scale system as a "full-frontal attack" against the middle class and Quebec's family policy.
"We believe rich people should pay more income tax." he said. "But child-care services and family policy are geared to everybody. And it isn't true that you're rich when your family income is $75,000."