The letter also said that Lion Capital would nominate Lyndon Lea, one of its founders, to the clothing retailer's board of directors to replace one of its previous designees, Gene Montesano. Lion Capital, a former lender to the retailer, has the right to nominate two of American Apparel's nine board seats. Lea had previously been on the board but stepped down in 2011.

Lion Capital also has warrants to purchase up to 12 percent of the retailer.

The letter, which is being reviewed by the board, asks the board to form a special committee to evaluate options, according to the source, who asked not to be named because the matter is not public.

Representatives for American Apparel and Lion Capital did not immediately respond to a request for comment.

Irving Place Capital has put in a bid for the retailer for up to $1.40 a share, an offer that American Apparel's board believes is far too low, Reuters has reported.

The Los Angeles-based company has been bogged down by debt and investigations into the conduct of former chief executive Dov Charney that had dragged out for months. Charney was fired on Dec. 16 after a six-month suspension and will be replaced by Paula Schneider, president of ESP Group Ltd.

The Wall Street Journal first reported the news about Lion Capital's letter late Sunday.

(Editing by Eric Walsh)

By Jeffrey Dastin