Wates is claiming the cash for extra work carried-out on The Malls for Basingstoke and Deane Borough Council last year.
The council has spent £6.2m on the refurbishment and have described the extra claims as “disappointing and concerning”.
Councillor John Izett, Cabinet member for property and finance, told This is Hampshire: “The contractor is claiming £2.3m more in scheme costs than the currently valued position, but the council’s contract team disputes the scale and validity of the contractor claims.
“At this stage in a contract, it is not unusual for there to be a difference between client team and contractor over the value of works completed, and it is part of the contract process to determine final costs.
“It is nevertheless disappointing and concerning that the contractor has decided to make such a substantial claim. If there is any substance to this claim, we will need to understand how it has arisen.”
Cllr Izett said there were a number of unforeseen problems, such as extra structural works to the lift shaft by The Anvil theatre, which were only uncovered when the area was stripped.
A Wates spokesman said: “We are currently working with Basingstoke and Deane Borough Council and hope a resolution is reached by the end of the year.
“As a locally-based business, we are committed to working on great schemes which benefit the local Basingstoke community.”