The Competition and Markets Authority said in its provisional findings last month that Murdoch's bid raised media plurality concerns because the deal would give his family too much control over United Kingdom news media.
21st Century Fox has vowed to maintain the editorial independence of Sky News and to continue funding the loss-making channel for a period of five years in an effort to dampen regulatory concerns at its looming takeover.
Opponents of the deal also contend that the Murdochs and Fox, in light of sexual and racial harassment scandals at Fox News in the USA, would not be suitable owners of Sky, though this argument has been rejected by regulators.
The Competition and Markets Authority (CMA) regulator had provisionally concluded in January that the takeover would hand too much power over British media to Murdoch.
The response came after the CMA recently ruled that if Fox's takeover of Sky "went ahead, as now proposed, it is likely to operate against the public interest", and set out a series of potential options, including insulating Sky News from Murdoch Family Trust.
The US-based media group has tabled a package of what it described as "firewall remedies" to the Competition and Markets Authority (CMA), including a pledge to establish an independent Sky News editorial board that would remain free of any influence by 21CF employees.More news: Big Love star Bill Paxton's family files wrongful death lawsuit
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Fox's proposals regarding Sky News were made in response to the list of possible remedies, and were released by the CMA.
An added complication is that Disney has agreed to buy most of Fox's business, and therefore may end up owning Sky.
While speaking at Recode's Code Media event on Monday, 21st Century Fox president and Fox Networks group chairman Peter Rice said he thinks his company is "a great fit for Disney".
If the Sky-Fox deal does finally go through, the whole of Sky would be likely to transfer to Disney's ownership.
The CMA's final report will be submitted to culture Secretary Matt Hancock by 1 May, and he has said he will make a decision on the deal by 14 June.