The case, which has been lodged under the comedian's real name, David Edward Williams, is listed as dealing with data protection.
No further details have been disclosed and FremantleMedia declined to comment.
The 52-year-old was replaced as a judge on the show with Bruno Tonioli, after he apologised for making "disrespectful comments" about contestants during breaks in filming.
Walliams was a judge on the talent show from 2012, with the comments being made in January 2020.
According to a leaked transcript seen by The Guardian in November 2022, Walliams referred to an older performer as a "c***" three times when he was out of earshot.
The publication reported that a spokesperson for Thames TV, part of FremantleMedia, had said that though the production company regarded Walliams’ comments as private, his language was “inappropriate”.
In a statement at the time, Walliams said: "I would like to apologise to the people I made disrespectful comments about during breaks in filming for Britain's Got Talent in 2020.
"These were private conversations and - like most conversations with friends - were never intended to be shared. Nevertheless, I am sorry."
Walliams’ representatives have been approached for comment.
Want a quick and expert briefing on the biggest news stories? Listen to our latest podcasts to find out What You Need To Know...