A report recommending the mutual termination of the council's nine-year deal with the company will go before the local authority's cabinet on Friday, 24 November.
The move comes as part of the council's plan to save £90 million over the next three years following Government cuts.
If approved, the council and Amey will complete the mutually agreed exit by the end of January 2018.
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Cllr Ann O'Byrne said: "The highways contract with Amey LG did initially deliver savings but we believe more can be achieved by bringing the operations back in house.
"We have seen with other services such as street cleansing and refuse collections that insourcing can deliver savings which can be reinvested to make our money go further.”
Amey's Highways Business Director, David Ogden, said: "We have reached a mutual agreement with Liverpool City Council to end our highways contract early after both sides raised concerns about the sustainability of the contract.
"The financial environment has changed significantly since the signing of this contract and we both agreed that this is the best course of action for all."
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