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There’s speculation that Duke Aiona will run for mayor of Honolulu next year, and the Republican candidate for governor in the last two elections said Monday he would neither “confirm nor deny” the possibility.

But that didn’t stop Aiona, a former judge who served as Hawaii lieutenant governor from 2002 to 2010, from saying incumbent Kirk Caldwell has been a “terrible” mayor.

“He really is the consummate politician, and I mean that with all sincerity,” Aiona said of Caldwell. “He is basically like the direction of the wind — that’s where Kirk’s going to be. This homelessness issue has really unveiled that, really shown how he is as a public servant.”

Aiona did not elaborate, but addressing homelessness was a major part of his 2014 gubernatorial campaign platform and a focus of the administration of Republican Gov. Linda Lingle, under whom he served.

Aiona also took issue with how the mayor is doing regarding the Honolulu rail project. Ainoa does not support rail — “I feel the project is just too expensive,” he said — but he has said that if he had been elected governor he would not have stood in the way of a city project.

“But as a mayor of the city and county, it’s a little different story,” he said.

Caldwell served as managing director under Mayor Mufi Hannemann and succeeded him as acting mayor when Hannemann resigned to run for governor in 2010.

Caldwell then lost the election to fill the rest of Hannemann’s term to former city prosecutor Peter Carlisle.

In 2012, however, Carlisle finished third in the mayoral primary to Caldwell and former Gov. Ben Cayetano, who ran as an anti-rail candidate. Caldwell prevailed in the general election.

County mayors are nonpartisan positions.