Goya Foods is in late-stage talks to sell a majority stake to The Carlyle Group in a deal that would value the canned-foods giant at roughly $3.5 billion, The Post has learned.

The founding family of Jersey City, NJ-based Goya — whose rice, beans, olives and cooking oils are ubiquitous at grocery stores across the US — hired Goldman Sachs in May to explore its options in what was expected to be a $3 billion sale.

Sources said the process appeared to stall this summer as Goya chief executive Robert Unanue drove a hard bargain, insisting that America’s largest Hispanic-owned food company was worth as much as $4 billion.

As the process has unfolded, Unanue also made it clear he wants to remain in control of the fourth-generation family company, even in a sale leaving private equity firms as the only logical buyers.

The current plan is for Unanue to remain CEO after the buyout, according to a source close to the situation.

In the negotiations with Washington-based Carlyle, headed by billionaire David Rubenstein, Goya is being valued at a healthy mid-teens multiple to its Ebitda, or earnings before interest, taxes, depreciation and amortization, according to a source briefed on the talks.

Likewise, insiders say Carlyle appears ready to accommodate the sellers’ demand that the deal not saddle Goya with too much debt.

Private equity firms typically put down about 35 percent of the purchase price in equity and have the company borrow the rest. In the Goya deal, however, the percentage they put down will be more like 60 percent, a source said.

The founding family hasn’t been without its dramas. In 2004, Unanue forced out his cousin Andy Unanue as CEO, spurring Andy to sue in a New Jersey court case that got settled about a decade ago. The once-warring parties are now on decent terms, sources said.

Goya did not return calls. Carlyle declined to comment.