LOS ANGELES, Jan 28 (Reuters) - Supermarket mogul Ron Burkle and his investment vehicle Yucaipa Cos has proposed taking a controlling stake in U.S. luxury retail chain Barneys New York in exchange for a $50 million cash infusion, a source familiar with the matter told the Wall Street Journal.

A Yucaipa spokesman could not be immediately reached for comment. Details of the proposal were laid out in a Dec. 11 letter from Burkle to the former chief executive of Dubai's Istithmar World Capital, which owns the retail chain, the Journal reported.

Last November, Yucaipa purchased a large amount of Barneys debt from Citigroup Inc (C.N) at about 60 cents on the dollar, the Journal said.

The reported loan deal would leave Istithmar World Capital with a 20 percent stake in the chain, known for its pricey duds and semi-annual warehouse sales.

Istithmar hired restructuring advisory firm Perella Weinberg last year to help it mull options to shore up its financial position.

The luxury chain, with stores in cities like New York and Chicago, has struggled in the recession as even wealthy consumers cut back on spending.

Istithmar, a unit of Dubai World [DBWLD.UL], bought Barneys for $942 million from Jones Apparel Group (JNY.N) in 2007. It provided some additional funding to the chain in April of 2009, allowing it to pay for its shipments for the rest of the year. (Reporting by Gina Keating; Editing by Bernard Orr)