Triton Container International Ltd., owned by Chicago’s Pritzker family, is up for sale, the latest attempt at selling the container leasing company that could be worth about $1 billion, several sources familiar with the matter said on Friday.

The auction is the latest in a series of asset sales by the Pritzkers, one of the wealthiest U.S. families. They have been selling assets after a 2001 settlement agreement, in which 11 heirs set a plan to break up the family fortune.

Triton’s auction, which started in the summer, is in the second round and has attracted private equity buyer interest, the sources said. Bank of America Corp is advising on the sale, they said.

Triton, which began operations in 1980, also has drawn interest from Asian suitors, two sources said.

The names of the bidders couldn’t be learned.

Triton wasn’t immediately available for comment. A Bank of America spokesman declined to comment. The sources are anonymous because the auction is not public.

This is at least the second time Triton’s owners have tried to sell the company. In 2006, the Pritzkers had hired Goldman Sachs to sell the company. At the time, Reuters reported the company was worth $2.5 billion.

That price would include debt, one of the sources said on Friday.

Triton’s fleet of marine cargo containers, with an original equipment cost of about $3 billion, is one of the largest and youngest fleets in the industry, according to its website.

The Pritzkers have struck deals for several assets in the last few years. In 2006, the family sold smokeless tobacco company Conwood to Reynolds American for $3.5 billion.

That was followed in 2007 by the sale of 60 percent of manufacturing and services group Marmon Holdings Inc to Warren Buffett’s Berkshire Hathaway Inc. for $4.5 billion.

Late last year, the family took Hyatt Hotels Corp. public. And this year, Madison Dearborn Partners bought a 51 percent interest in credit reporting company TransUnion Corp. from the family.