Councillors will be asked to award the contracts to the company at a cabinet meeting on Friday, 19 May.
The schemes will see nine new classrooms and a kitchen added at Liverpool College. Following relevant approvals, work will begin in July with completion set for April 2018.
Elsewhere, three new classrooms will be built at Sudley Infant School along with a learning resource base, extra toilets and storage. Work will start in July with the scheme completed by February 2018.
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Further expansion works are set to get underway at Monksdown Primary in Norris Green.
The project's are being carried out due to rising birth rate and ongoing regeneration leading to further demand for school places.
Assistant Mayor and Cabinet member for education, Cllr Nick Small, said: "It's great that we're seeing more people moving in to the city, but it is vital parents have a good chance of getting their child into a nearby school of their choice.
"We are taking action now to tackle the areas where we know there is the greatest demand to alleviate some of the pressure.
"The schools that we have identified meet the Government's very strict criteria for this funding including being ranked as good or outstanding by Ofsted and on a solid financial footing."
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