Peter Thiel is demanding that he be given the chance to bid on Gawker.com, the gossip and news website he helped drive out of business and which is now being shopped in bankruptcy.

Lawyers representing Mr. Thiel said in papers filed Wednesday in the U.S. Bankruptcy Court in New York that the billionaire venture capitalist is “the most able and logical purchaser” of Gawker.com but that, so far, his overtures have been rebuffed by the administrator overseeing the sale process.

“Obviously, if Mr. Thiel is allowed to bid on a level playing field, value will be maximized; if not, it won’t,” lawyers for Mr. Thiel said. The filing says Will Holden, a managing director at Dacarba LLC, the firm overseeing the sale process, should be required to afford Mr. Thiel “a fair opportunity to submit a competitive bid.”

Wednesday’s filings were first reported by Buzzfeed News.

Mr. Thiel’s interest in the website, which has been dormant since August 2016, adds a new twist to the continuing legal wrangling between him and publisher of the blog, Gawker Media LLC. Mr. Thiel secretly financed Hulk Hogan’s lawsuit against the publisher, the ruling on which by a jury forced the Gawker Media and its founder Nick Dentoninto chapter 11 last year and, ultimately, out of business.