Berkshire LLC submitted by far the highest bid — more than $1 billion — for the 5,881-unit Brooklyn housing complex Starrett City, according to two sources familiar the deal. Last night, work on finalizing the deal extended late into the evening.

Billionaire developer Lev Leviev controls Berkshire LLC. Also a diamond trader, Mr. Leviev is a former partner of active New York developer Shaya Boymelgreen and the owner of Africa Israel Investments, a publicly traded company.

Bids were due Monday evening on what is known as the largest federally subsidized rental project in the country, with 46 towers on about 140 acres.

Governor Spitzer, along with tenants groups and the president of Brooklyn, Marty Markowitz, have said they will resist attempts of a new owner raise rents to help pay the billion-dollar-plus price tag. Starrett City Associates has said the rents will remain affordable.

The state controls Starrett City’s $234.4 million interest-free mortgage and can approve or reject any new owner.

The winning bid appeared to be well above the bids of several active players in New York real estate. The Related Companies and Apollo Real Estate Advisers are among several companies that bid less than a half of the winning total, according to a source.

A source familiar with the deal said the winning bid is contingent on a set of potentially arduous conditions, including the ability to develop more apartments on the property, which would require government approvals.

A spokesman for the group that owns the complex, Starrett City Associates, denied that a deal had been finalized.

“They are sitting down there, going over the bids right now,” Martin McGlaughlin, said late last night.