Voting is due later to decide whether North Somerset Council supports a single directly-elected "Metro Mayor" mayor for the West of England.
Four West councils, including Bristol, South Gloucestershire and Bath and North East Somerset, were offered the idea in the Chancellor's March Budget.
Nearly £1bn would be invested over 30 years to fund projects in key areas such as roads.
If North Somerset rejects the move, other councils would renegotiate.
In September, Conservative-run North Somerset said it opposed the plans.
It said instead it would continue to "urge central government to offer far greater control of local finances to local authorities, including the further localising of business rates".
A meeting due at 18:00 BST will also hear the views of residents and parish councils.
Fears have been raised about a "Bristol-oriented authority" with smaller villages overlooked, and the re-creation of the old Avon-wide authority.
Bristol City Council and South Gloucestershire Council have indicated that they support devolution, while Bath and North East Somerset Council has not yet stated a preference.
If the deal is agreed, a new mayor to chair a West of England Combined Authority would be elected in May 2017.