Business Secretary Vince Cable is to announce plans to give the lowest-paid apprentices a £1.06 an hour pay rise.
The move is backed by the Conservatives and could come into effect next October, if cleared by regulators.
Liberal Democrat Mr Cable will unveil the plan at his party's annual conference in Glasgow later.
He is also expected to defend the benefits of immigration, saying his party has a responsibility to be the voice of "sanity" on the issue.
He will also use his speech to activists to launch a fierce attack on the Conservatives over their proposed benefit freeze.
Mr Cable is writing to the Low Pay Commission recommending that the apprentice rate of the minimum wage and the 16/17-year-old rate are combined.
Most apprentices already earn more than the minimum wage but about 31,000 people are expected to benefit from the move, with their hourly rate going up from £2.73 to £3.79.