Weiner announced his resignation Thursday, apologizing for the personal mistakes I have made and the embarrassment I have caused."
Several potential Democratic and Republican contenders say they've been approached about the job, although none have declared their candidacies formally amid uncertainty over how the seat will be filled once redistricting maps are completed, the New York Daily News reported Friday.
Redistricting could eliminate Weiner's district that represents Queens and Brooklyn.
"At least for the next year and a half that that seat is in existence the district is going to need a very capable, aggressive legislator to represent the needs of the district," said state Assembly member Rory Lancman, a Democrat from Queens. "The thought of doing it is very sobering."
New York Gov. Andrew Cuomo could declare a special election or allow a traditional primary in which candidates gather signatures to get on the ballot. He hasn't indicated what he will do, the Daily News said.