The business secretary's plan would see the national minimum wage for apprentices, which went up 2% to £2.73 per hour on 1 October, unified with that for 16-17 year olds, which also rose 2% to £3.79 per hour.
While the majority of apprentices are already paid more than the minimum wage, the proposed rise would mean around 31,000 apprentices would receive a pay rise of more than £1 per hour.
According to the Liberal Democrats, the proposal will help employers by simplifying pay structures.
Cable said: "The national minimum wage has successfully protected the incomes and jobs of the lowest paid workers in the UK. This year it will see the first above inflation rise since the recession.
"Thanks to the Lib Dems, apprenticeships are helping to create a stronger economy and opportunities for young people. I want the minimum pay for apprentices boosted by £1 an hour."
The proposal, which is backed by the Conservatives, will be put to the Low Pay Commission (LPC), the independent body that advises government on the national minimum wage, ahead of its annual recommendation on the national minimum wage next spring.
The government will then decide on any changes to the national minimum wage, based on the LPC's recommendations.