American Apparel Inc's board is increasingly open to letting its ousted founder, Dov Charney, stay at the company, Bloomberg reported, citing people familiar with the matter.

The U.S. retailer is also considering giving Charney a new role, Bloomberg reported. He currently serves as a consultant to the company.

American Apparel's shares were up 2.4 percent in extended trading.

American Apparel said on Monday it hired Scott Brubaker, a managing director at turnaround firm Alvarez & Marsal, as interim chief executive, replacing John Luttrell, who had been serving as both interim CEO and CFO since Charney's exit.

Luttrel's departure could make it easier for Charney to make a come back, Bloomberg said. Brubaker has also been in talks with Charney, the news service reported.

Charney, who was removed from the chairman and chief executive position in June for alleged misuse of corporate funds and his role in disseminating nude photos of an ex-employee, in July joined hands with hedge fund Standard General LP and raised his stake in the company to 43 percent.

The hedge fund and Charney soon thereafter reached a deal with the company to remake its board and bolster its finances.

Standard General gained control of Charney's entire stake after Charney transferred it to the hedge fund as collateral for a loan.

The hedge fund, which also has voting rights over Charney's stake, is leading the company's efforts to avoid bankruptcy.

American Apparel was not immediately available for comment.