To alleviate those fears, Fox has proposed further "firewall remedies" that include a commitment to set up an independent editorial board for Sky News, a well-respected news outlet.
British regulators have recommended that the government block Fox's purchase of Sky because it would Murdoch too much control over the country's media.
21st Century Fox says it is willing to commit to a Sky-branded news service for at least five years.
The "firewall remedies" were revealed in documents published by the Competition and Markets Authority (CMA).
Fox has been trying to buy the 61% of Sky that it does not now own.
Fox's proposals regarding Sky News were made in response to the list of possible remedies, and were released by the CMA.
21st century Fox has said that as result of said proposals, "there could be no circumstances in which, post-transaction, the MFT or members of the Murdoch family could influence, whether directly or indirectly, the editorial line or policy of Sky News".
It also said it agreed with the CMA's view that the possibility of Disney buying Fox assets, including its stake in Sky, should be taken into consideration.
Murdoch already owns three of Britain's biggest newspapers: The Sun, The Times and The Sunday Times. The CMA's final report on the takeover bid will be with Hancock by 1 May.
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 proposed remedies (.) decisively eliminate the source of the CMA's provisional concerns - potential MFT influence over Sky News' editorial decision-making", it said. Opponents of the deal also contend that the Murdochs and Fox, in light of sexual and racial harassment scandals at Fox News in the US, would not be suitable owners of Sky, though this argument has been rejected by regulators.