The business is cutting about 80 positions in the first quarter.
Burberry has been the subject of takeover speculation for the past six months.
The $650 million deal was funded through a combination of cash, common stock and a junior lien seller note.
Piquadro acquired 80 percent of the brand for a sum of $3.46 million.
Marvin Traub Associates is helping with expansion plans.
The investment firm sees strong potential for the French underwear label in the affordable luxury segment.
Permira’s first consumer tech investment in Germany revolves around the invitation-only shopping club Bestsecret.com.
Brand management firms are said to be taking a close look at American Apparel.