Gawker Media has hired an investment banker to explore strategic options including a potential sale, according to a person familiar with the matter, as the digital media company fights a costly legal battle with professional wrestler Hulk Hogan.

The digital publisher has hired banker Mark Patricof of Houlihan Lokey as it reviews its options, Gawker confirmed Thursday.

Terry Bollea, known in the wrestling world as Hulk Hogan, sued Gawker for violating his privacy by posting a clip of Mr. Bollea having sex with the ex-wife of a former friend.

In March, a jury awarded the wrestler $140 million in damages. Gawker is appealing the ruling.

Late Wednesday, Silicon Valley billionaire and investor Peter Thiel acknowledged that he has been providing financing for Mr. Bollea’s legal fight and other such battles involving people who Mr. Thiel feels have been targeted unfairly by the media company.