The New York Post said Farrow and her estranged adopted daughter Soon-Yi Previn were initially listed as potential witnesses in the case, but Dov Charney, the clothing company's boss, has since pledged not to dredge up Allen's personal life during the proceedings and therefore won't allow his lawyers to call Farrow or Previn to testify.
Allen and Farrow famously broke up after Farrow discovered Allen had been having an affair with Previn. The split was followed by a messy custody battle over the three children Allen and Farrow shared.
Allen and Previn are now married and the parents of two children.
The Oscar-winning writer-director-actor is suing American Apparel in Manhattan federal court, claiming his image was used on billboards without authorization, the Post said.