Lazio, of Brightwaters, is expected to capture more than half the votes at the Republican nominating convention in late spring. He already has the backing of 14 county leaders who together represent 41.2 percent of the vote.
Lazio also has picked up support from at least eight Conservative Party leaders. No Republican has won statewide office without the Conservative ballot line in recent memory.
"Rick is, at the moment, the only candidate out there," Cox said. "It looks like he's going to get the majority of the weighted vote of the county chairs . . . We're going to be working with him."
Cox had wooed other potential candidates who had more money and name recognition, including Erie County Executive Chris Collins. But in a letter Tuesday, Collins told Cox he had decided against pursuing the Executive Mansion this year.
Cox, who summers in Westhampton Beach, also has met with Levy. Asked Thursday about Levy's chances of winning the GOP nomination for governor, Cox said, "What happens with that I don't know. I do know that Rick has done an awfully good job over the last year carrying the Republican banner."
Levy said he would be "very respectful" if Cox and others back someone else. However, he added, "if their front-runner this year fails to take root - as was the case in 2006 - they still know there is someone out there with the passion, the proven fiscal record and the consistent, detailed plan to overhaul the state's dysfunctional government."
Separately Thursday, Levy called for the establishment of a financial control board to oversee New York State's shaky finances and for a cap on state spending. He also said the governor should have unilateral power to impound spending approved by the legislature.
The proposals have little support in the Capitol. A spokesman for the Senate's Democratic majority called them "distractions." Aides to Assembly Speaker Sheldon Silver (D-Manhattan) and Paterson declined to comment.