Suffolk Democratic Chairman Richard Schaffer said he doubts his party can name candidates for county district attorney and sheriff by Monday’s party convention because county GOP chair John Jay LaValle has raised the surprise possibility of a cross-endorsement deal this year.

“The Republican leader indicated he may be open to cross-endorsements for countywide positions and we have to explore that,” said Schaffer. “There are so many moving pieces, I don’t know if we can get it done by next Monday.”

The potential delay comes after Democrats on Saturday screened seven potential contenders for district attorney — including Police Commissioner Tim Sini and David Calone, a former county planning commission chairman — in a marathon six-hour meeting at Democratic headquarters in Bohemia.

Schaffer said LaValle first raised the prospect of a cross-endorsement last Wednesday in an informal meeting at the gym where Schaffer’s works out in Farmingdale. The GOP leader did not disclose names of candidates he might support, Schaffer.

LaValle did not return calls for comment Monday.

The county GOP convention is June 5, the day before nominating petitions can first hit the street.

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LaValle on last Tuesday told the 10 GOP town leaders he wanted to lift for a ban on major party cross-endorsements that he advocated two years ago to protect “Republican principles and ideals.”

Several GOP officials said LaValle wanted to lift the ban for a year because East Hampton and Shelter Island Republicans were having difficulty coming up with enough candidates for town races.

Schaffer, who has no sheriff candidates of his own, said he is holding separate cross-endorsement discussions with the Suffolk Conservative Party, which has nominated State Sen. Philip Boyle (R-Bay Shore) for sheriff.

Schaffer said he could back Boyle, but also has two sheriff contenders he declined to name.

Republican leaders on Wednesday will screen GOP sheriff candidates including Boyle, Stony Brook University deputy police chief Larry Zacarese and Fred Sales, a former Suffolk County police officer. Steve Kuehhas, a Suffolk undersheriff and district attorney, also wants to be screened.

Schaffer also said the party screening committee will hold a conference call or meet to narrow the field of DA field and hold final interviews with top contenders.

If a decision comes after the convention, the party committee normally votes to let the chairman make the final choice.

Sini said last week he intended to keep his $162,000-a-year job as commissioner during the campaign and “do whatever it takes to get on the ballot.”

Schaffer said he had no problem with Sini remaining as commissioner while seeking office, and said he believes Democrats will avoid a divisive primary.

“My job is to avoid a primary,” said Schaffer. “I think enough was said in interviews so that all the candidates will eventually get behind the one that the party believes will be the strongest candidate.”