The state government is using taxpayer-funded telephone surveys to gauge residents' support for council mergers in parts of Sydney where the policy has become a political headache for the new premier.

The telephone surveys, which were commissioned by the Department of Premier and Cabinet, were conducted over the past week as the Berejiklian government considers whether to change its council merger policy.

Premier Gladys Berejiklian's cabinet met for the second time on Thursday, but it is not known whether council mergers were discussed.

Among the areas surveyed was Mosman, where dissatisfaction over a proposed merger with North Sydney and Willoughby councils is expected to hurt the government at the upcoming by-election for the seat of North Shore. The seat was vacated after the resignation of dumped minister Jillian Skinner last month.