Unite officials claim the contractor is cutting terms and conditions for workers and looking to reduce union recognition on the contract.
But Amey has flatly denied the claims and is urging further talks to head off any threat of industrial action.
Unite regional co-ordinating officer Andy Fisher said: “Industrial action would be the last resort and would not be entered into lightly as it will cause incredible disruption across the North West.
“However, Amey needs to understand that Unite will not allow its members to be treated in this manner.”
An Amey spokesperson said: “Unite are an important stakeholder to the Amey business and we remain absolutely committed to working collaboratively with them to ensure the health, safety and wellbeing of our employees.”
“We agree with Unite that industrial action should be a last resort, not least in order to avoid significant disruption to road users.
“However we disagree categorically with the suggestion that we are either seeking to change our existing employees’ terms and conditions or to end union recognition.”
“We would look to reach quick resolution that is acceptable to all and would welcome the opportunity for positive dialogue with Unite or ACAS mediation to achieve this.”