In his speech to the Liberal Democrat party conference in Glasgow, Cable will lay out the plans to raise the base rate of pay from £2.73 per hour to £3.79. It would come into effect on 1 October 2015.
October is traditionally the month all rates of minimum pay are adjusted in the UK. On 1 October this year apprentices saw a modest increase of 5p per hour to their minimum pay.
The move would bring pay for apprentices in line with the current minimum rate for workers aged 16 and 17-years-old. Cable is to put the proposal to the Low Pay Commission for approval later this year. It is estimated 31,000 apprentices will benefit from the proposed change.
In today's speech Cable is expected to praise the impact of the minimum wage to protect "the incomes and jobs on the lowest-paid workers in the UK". He is also expected to say that apprenticeships are "helping to create a stronger economy and opportunities for young people".
Confederation of British Industry deputy director-general Katja Hall hailed apprentices as "part of the answer to solving the UK's skills crisis". But she advised caution on any increase in pay.
"Too few apprenticeships at the moment go to the young and relatively unskilled," she said. "Companies already pay their share into training, so raising the cost of taking these young people on would be unwise and put off many smaller firms from getting involved."