State Democrats will hold their party convention in Melville next month, party sources said, highlighting the importance of Long Island and other suburbs to Gov. Andrew M. Cuomo's re-election campaign.

A source also said that Kevin Law, president and CEO of the Long Island Association and a former Suffolk chief deputy county executive, has been approached by Cuomo intermediaries to consider running for lieutenant governor, a job held by former Rochester Mayor Robert Duffy.

The choice of Suffolk as the convention site highlights the importance of the suburbs in Cuomo's bid to bring in big re-election numbers to bolster possible presidential aspirations and counter Westchester County Executive Rob Astorino, his likely GOP opponent.

The convention is planned for May 21-22 at the Huntington Hilton.

"Having the convention in Suffolk County demonstrates how important the suburbs are to the governor, and with the success of the tax cap I'm sure he'll do quite well here," said Deputy County Executive Jon Schneider.

There is widespread speculation that Duffy won't be on Cuomo's 2014 ticket.

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Cuomo has repeatedly skipped chances to say Duffy will remain. Also, Duffy briefly sought a job leading the Rochester Business Alliance but withdrew when his name became public. He recently said he regretted leaving the city.

Law has led the LIA, the Island's largest business association, since 2010. From 2007-10, he ran the Long Island Power Authority. He also once served as deputy to Suffolk County Executive Patrick Halpin, where Law worked with Larry Schwartz, now Cuomo's top aide.

Law couldn't be reached for comment Friday.

The choice of Suffolk for the state convention marks the second time Suffolk Democrats will host the event since Suffolk Democratic chairman Richard Schaffer took over as county Democratic leader in 2000.

The state convention in Hauppauge in 2006 came shortly after then-Attorney General Eliot Spitzer had defeated Nassau County Executive Thomas Suozzi in a state Democratic gubernatorial primary. The two men in a symbolic fence mending shook hands before hundreds of party activists.

Schaffer has longtime ties to the Cuomo family dating to when he attended the State University at Albany with Cuomo's sister, Madeline. As a college student, Schaffer also was a volunteer for then-Lieut. Gov. Mario Cuomo in 1982 when Cuomo upset the late New York City Mayor Ed Koch in the Democratic gubernatorial primary. Schaffer was the first county leader statewide to endorse Andrew Cuomo's gubernatorial bid in 2010.

Cuomo also is scheduled to headline Suffolk Democrats' spring dinner April 28 at Villa Lombardi's in Holbrook. The $300-a-head event typically attracts more than 500 people.