BY ANUPREETA DAS AND GINA CHON

One of America’s wealthiest clans, the Pritzker family, is continuing to shed assets with the expected sale of Triton Container International Ltd. to private equity firms Warburg Pincus LLC and Vestar Capital Partners, said people familiar with the matter.

The two buyout shops are close to a deal to acquire the shipping-container leasing company owned by Chicago’s Pritzker family for about $1 billion, these people said.

The Pritzkers, which took the Hyatt Hotels Corp. hotel chain public in 2009, are among the wealthiest U.S. families, controlling a business …