The newly formed Cheshire West & Chester council is in talks to sell County Hall to Chester University and relocate to Liberty's HQ development nearby.
Cheshire West & Chester would take the entire 82,000 sq ft office element of the new mixed-use building, due for completion in the autumn.
Leaked council documents said the 50-year-old County Hall is no longer deemed fit for purpose by the new authority.
The six former borough councils and the county council of Cheshire were reorganised into two new unitary authorities for Cheshire East and Cheshire West & Chester in April.
The local authority in the west occupies 20 offices and wants to reduce this figure by more than half.
Chester University is rumoured to be considering a £10m offer to buy County Hall, which is partly owned by Cheshire East council.
A final decision on the fate of County Hall and the council's proposed move to HQ is due as early as the end of August.
As well as offices, HQ will contain apartments, restaurants and an Adobe hotel overlooking the Chester Racecourse.
HQ is being built by Cheshire-based construction firm Pochin. Legat Owen and Savills are joint agents on the offices.
All parties declined to comment.