High-level Democrats are urging North Hempstead Town Supervisor Judi Bosworth to consider a bid to succeed Rep. Steve Israel in the 3rd Congressional District, sources said Wednesday.

Bosworth, who has shown little interest in running, was being recruited because some party officials fear that the best-known Democrats currently are seeking the seat, including former Nassau County Executive Thomas Suozzi, wouldn’t fare as well against the leading Republican hopeful, state. Sen. Jack Martins of Old Westbury.

“She’s immensely popular throughout the biggest geographical area of the district,” a Democratic source said of Bosworth, a former Nassau County legislator from Great Neck who was elected supervisor in 2013, and re-elected last year by a 35-point margin.

More than 50 percent of Third District voters live in Nassau, with the remainder in Suffolk and Queens. Israel (D-Huntington) announced this month he would not seek a ninth term.

Bosworth was not available for comment Wednesday, a spokeswoman said.

Nassau Democratic chairman Jay Jacobs said Bosworth “certainly is interested in looking at her options.

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“There is not a more popular elected official, past or present, than Judi Bosworth, and frankly that would certainly add a new dynamic to the mix,” said Jacobs, who has also been one of Suozzi’s biggest backers.

Told of the effort to draft Bosworth, Suozzi called her a “fantastic public servant who is involved for all the right reasons.”

On Wednesday, potential Democratic candidates met with Democratic Party leaders including Israel, Jacobs, Suffolk chairman Richard Schaffer and Queens chairman Rep. Joseph Crowley.

They were Suozzi; former North Hempstead Supervisor Jon Kaiman; Democratic National Committee member Robert Zimmerman; North Hempstead Town board member Anna Kaplan; Suffolk County legislators Steve Stern and William Spencer; former Suffolk Legis. Jon Cooper; psychologist and philanthropist Laurie Scheinman; businessman Todd Richman, accounting firm executive Jerry Cohen and attorney Jonathan Clarke.

“The one good thing that came out of today is that we started the conversation of having the strongest Democrat, so we can put our best foot forward,” Schaffer said.

“The Democrats have nearly a dozen candidates that screened today, yet none of them appear to be up to the challenge to run against Jack Martins,” said E. O’Brien Murray, a Martins spokesman, citing the wooing of Bosworth.

Martins considers Bosworth a friend and “has worked well with her,” Murray said.

With Rick Brand and Robert Brodsky