Retailleau is the leader of the Les Républicains party.
He has not endorsed either incumbent mayor Christian Estrosi or rival Eric Ciotti.
The situation highlights divisions within the right-wing political spectrum.
Briefing: In Nice, right-wing leader's refusal to choose between the right and far right sows confusion
Strategic angle: Bruno Retailleau's indecision complicates the political landscape ahead of the elections.