CHICAGO (Reuters) - The bankruptcy estate of Lehman Brothers Holdings Inc is preparing to make a $1.33 billion bid for part of apartment owner Archstone that it does not already hold, according to a report in the Wall Street Journal.

The Wall Street Journal, which cited people familiar with the matter, said the bid Lehman was putting together was for a cash deal.

The move was designed to keep real estate mogul Sam Zell from buying a piece of the company, which owns stakes in 77,084 apartments in major cities across the U.S. and Europe.

Lehman, which already owns 47 percent of Archstone, is looking to buy another 26.5 percent in the deal.

Zell's Equity Residential agreed to buy 26.5 percent, or half the interest Barclays Plc and Bank of America Corp hold in Archstone for $1.325 billion earlier this month.

But Lehman dismissed the Equity Residential deal as too low, ill-timed and in violation of its agreements with its co-owners.

(Reporting by Mark Weinraub; editing by Anthony Boadle)