If Attorney General Andrew Cuomo chooses to run for governor, he would leave his current post open for ambitious local politicians - such as Levy and Suozzi, both Democrats.
"Both Suozzi and Steve Levy would do anything to get out of their particular jobs," said Hank Sheinkopf, a Manhattan-based Democratic consultant. "There are going to be two opportunities that are clear."
The second opportunity comes with the lieutenant governor's office, which was vacated by Paterson in March 2008 when he succeeded Gov. Eliot Spitzer, who resigned in a prostitution scandal. The party's candidate for lieutenant governor is typically selected by the candidate for governor, though a primary is possible.
Neither Suozzi nor Levy is expected to challenge Comptroller Thomas DiNapoli, a Great Neck Plaza Democrat, the observers said.
While Levy and Suozzi insist they are focused on the jobs they have - Suozzi is seeking a third, four-year term as county executive Nov. 3 - both have ambitions beyond county lines. Levy declined to comment for this story; Suozzi did not respond to requests made through his office.
"Steve could be a natural candidate for the attorney general position," said Suffolk Democratic chairman Richard Schaffer, Levy's most prominent supporter. "Steve is definitely someone who should be taken seriously because of his appeal."
Levy, 50, and Suozzi, 47, have certain drawbacks as statewide candidates, experts said.
Suozzi, whose father is a law partner with Paterson's father, is seen as close to the governor and could suffer from having two downstate Italian Catholics potentially on the ticket - Cuomo, from Queens, and DiNapoli. "It would be hard to run three men from downstate and Long Island with Italian Catholic names," a top Long Island Democrat said.
Levy's hard-line stance on illegal immigration could cost him support, especially in Hispanic neighborhoods, experts said.
Suozzi and Levy also are relatively unknown statewide, which could make fundraising difficult, the experts said. Levy has $3.8 million in campaign funds and Suozzi, $2.8 million, according to the most recent filings.
Lee Miringoff, the director of the Marist Institute for Public Opinion, said he hasn't polled either's chances in a statewide race since Suozzi's failed 2006 run for governor, when he lost the Democratic primary to Spitzer.
But that 2006 experience may help Suozzi in a second statewide race. "You've met people, you've developed a list of potential supporters," Miringoff said. "There's nothing like the experience of having been around the track."