Wakefield Council says it has had "no notice" from UNISON that its members are prepared to strike.
Staff at the local authority, who are represented by the trade union, have voted in favour of taking industrial action in response to changes to the council's sickness policy.
Further votes have to take place, however, before any walkout happens.
But in a statement on Wednesday, Wakefield Council's chief executive Merran McRae said, “The council has received no notice from the union of either a strike or whether members were prepared to strike."
An official from UNISON, which represents around 4,500 of the authority's 11,000 workers, described relations between the two parties as "tense" on Tuesday, after news of the ballot became public.
UNISON says the new policy, which was imposed by the council in May, will make it easier for them to sack workers who are on long-term sick, or have disabilities.
The council disputes that, and describes the new policy as "caring" and one which will make life fairer for its workforce.
Among the changes that have been put in place are the removal of review meetings for staff on long-term sick, and the introduction of "attendance targets" for absentees.
The local authority also says it consulted with both UNISON and the Unite union about the changes, but claimed invitations to meetings were not taken up.
UNISON argues that they had no notice about the meetings.
Unite has yet to publicly offer their response to the sickness policy.
The GMB union was not consulted about the changes, as although it has members working for the council, it is not yet recognised for collective bargaining.