The communications regulator has received a letter from the Department for Digital, Culture, Media and Sport asking for more input before the Culture Secretary Karen Bradley decides whether the proposed purchase should face an in-depth investigation.
Fox, the international film and television giant behind hit shows like The Simpsons and Modern Family, already owns a 39.1% stake in Sky.
It tabled a proposal just before Christmas to buy the remainder of the company for £11.7bn, valuing the whole of Sky at £18.5bn.
Ms Bradley said in July that she was "still minded" to refer the bid to the Competition and Markets Authority after a report from Ofcom flagged up "public interest concerns" regarding media plurality.
The DCMS now says Ofcom has been given two weeks to respond and is expected to do so before 25 August.
In a statement, it said: "After assessing the large number of representations made in relation to the Secretary of State's referral decision, a number of these raise new evidence and/or comment on the Ofcom assessment.
"Any referral decision by the Secretary of State must be taken on the basis of a valid assessment of all the relevant evidence.
"For this reason the DCMS has asked Ofcom to advise on a number of points arising from these representations."
Responding to this, an Ofcom spokesman said: "We have received the department's request for further clarifications and will respond within the requested time."
Ms Bradley asked Ofcom in March to investigate, under the 2002 Enterprise Act, whether the takeover was in the public interest on the grounds of media plurality and broadcasting standards.
The plurality issue concerned whether the Murdoch family, which is a major shareholder in both News Corp - the owner of The Sun, The Times and the Sunday Times - and Fox, would emerge from a takeover with too large a share of the UK news market.
Together, News Corp and Fox would own just three of the top 15 UK news providers by audience reach - Sky News, The Sun and the Sky News website. The BBC alone, meanwhile, accounts for seven of the top 15 providers.
The broadcasting standards strand of the investigation was an assessment of Fox's commitment to uphold UK broadcasting standards.
If Ms Bradley decides the takeover would be against public interest, she can then refer the takeover to the CMA for a full review, a process that would take six months.
Alternatively, she may decide to allow the deal to go ahead, or allow it to go ahead subject to Fox meeting certain conditions.
Sky first received a takeover approach from News Corp, then the owner of Fox, in June 2010.
That bid was also referred to Ofcom, which agreed to allow the deal to go through, provided Sky News was spun off into a separate company.
However, the following July, the bid was dropped following public anger at revelations that the News of the World had hacked the mobile phone of murdered teenager Milly Dowler.
News Corp subsequently demerged into two businesses: News Corp and 21st Century Fox, whose only UK asset is currently its existing share of Sky.