The group UK arm, which has three stores in Birmingham, Liverpool and London, is expected to appoint the advisory company RSM as administrator on Monday.
The stores, the first of which opened in 2010, employed more than 290 people, according to the latest published accounts, which cover the year to February 2017 when the business made a £61m loss on sales of £26m.
Chapter 11 provides struggling companies with protection from their creditors, giving management time to implement restructuring plans.
Forever 21 difficulties reflect the problems afflicting traditional retailers on both sides of the Atlantic.
Since the start of 2017, more than 20 major US retailers, including Sears and Toys R Us, have filed for bankruptcy as more customers shift to online retailers such as Amazon.
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Founded in 1984, Forever 21 has 815 stores in 57 countries. Last week, the retailer said it would stop trading in Japan and close all 14 stores there at the end of October.
The company plans to leave most of its locations in Asia and Europe but will continue to operate in Mexico and Latin America.