Federal investigators are reportedly probing an alleged hack that compromised Fox News' internal systems, resulting in the release of previously unaired footage featuring its former star host, Tucker Carlson.
The paper reached out to Mr Burke for comment, but he said his lawyers advised him against speaking about the matter.
Mr Burke has not been accused of any wrongdoing.
Fox News received a letter from Assistant US Attorney Hay Trezevant requesting that it maintain any records related to its investigation for at least 90 days. The letter reportedly identified the network as "one of the potential victim-witnesses" of the alleged hack.
Carlson was fired from Fox News in April, after which several previously unaired videos of him were leaked to the press.
The footage at the heart of the hack investigation related to a Vice News story titled "Watch the Disturbing Kanye Interview Clips that Tucker Carlson Didn't Put on Air," as well as a video series titled "FOXLEAKS" published by Media Matters.
The Vice News story includes unaired portions of Carlson’s two-part interview with West, who makes disturbing comments about Jewish people.
The FOXLEAKS videos show Carlson speaking candidly between commercial breaks and before segments on his shows.
On 5 May, Fox News sent a cease-and-desist letter to Media Matters over its FOXLEAKS compilation, which included unaired footage of Carlson.
The network also sent a letter to Dominion Voting Systems demanding it conduct an internal investigation after leaks connected to text messages Carlson sent were made public. Fox recently agreed to a $787m settlement with Dominion to end a defamation lawsuit the ballot technology company brought against the network following the 2020 election.
Numerous text messages from Fox News personalities were made public during the discovery process in the Dominion trial, including some that originated from Carlson. There are some communications that were not made public, which only Dominion's lawyers, Fox News, and Carlson would know exist.
Carlson has accused Fox News of leaking the negative material about him.
The Independent has reached out to Fox News for comment.
Since his firing, Carlson has announced he plans to begin broadcasting a new show on Twitter.