It is estimated the road would cost around £95m, with the department for transport asked to contribute about half of the costs.
Cooper attended the meeting along with Congleton MP Sarah Russell.
The Middlewich bypass would be a 1.6 mile single carriageway road and the project includes new bridges over the Trent and Mersey Canal, and the nearby railway line.
The case for the bypass was made in 2017 and it received planning permission two years later.
Preparatory work had already begun when the business case was rejected this year.
Cooper said: “Although the minister made no commitment that funding would be released for the project, we remain hopeful.
“There would also be benefits for transport locally as a bypass would reduce congestion and improve reliability of bus services, both of which would encourage businesses to the area.”
At the time of submitting the business case in September, Councillor Mark Goldsmith from Cheshire East Council said the bypass was “shovel ready”.
“Delaying this scheme further will have major financial implications for the council and to ensure that it remains achievable, our ambition is to receive full business case approval from government later this year, or early 2025, so that we could start on site in spring 2025 and the bypass can be open by autumn 2027,” he said.
