American Apparel has received a takeover offer from an unnamed party less than a week after the US retailer ousted CEO Dov Charney and named his successor.

The company said it will evaluate the $1.30 to $1.40 per share proposal, but "remains focused on positioning American Apparel for a successful turnaround".

The news came as the retailer named Colleen Brown as chairperson, after Allan Mayer and David Danziger stepped down as co-chairmen of the board.

"It's time to focus on the work ahead of us and push this company to reach its full potential," she said. "This is a pivotal moment for American Apparel, and I believe the company is poised for a significant turnaround."

Earlier this week, American Apparel adopted a so-called 'poison pill' stockholder rights plan - its second this year - which the company says is designed to strengthen the ability of the board to protect its shareholders.

The company last week appointed industry veteran Paula Schneider as its new chief executive, with effect from 5 January.