Last week, News Corp deputy chairman Chase Carey claimed that the firm's 700p per share offer for Sky is "full and fair", despite the bid being swiftly rejected by Sky's board.
Sky's directors, led by deputy chairman Nicholas Ferguson, indicated that 800p was the minimum offer level to start serious negotiations.
The board's stance is also backed by the majority of Sky investors holding the 60.9% of the firm not already owned by Rupert Murdoch's News Corp.
Despite Carey's comments, the majority of analysts and experts believe that the firm will increase its offer for Sky to complete the deal, reports The Financial Times.
The current bid of 700p would involve News Corp paying £7.37 billion for the remaining Sky shares, valuing the company at £12.27bn. However, an offer of 800p would increase the firm's outlay to £8.43bn.
Stephen Adams, head of UK equities at Aegon Asset Management, said: "Our view is that an offer in excess of £8 is needed. All the key metrics you would look at in an independent business look better now than prior to the bid."
However, a source close to Sky said that the firm's non-executive directors could drive up the price so high that News Corp may seek other solutions.
"The non-execs have not even agreed on 800p as the price they would accept," the source said.
"It could be 830p before they would recommend a bid to shareholders and perhaps News couldn't afford that. They could go hostile."
There is also concern within Sky that some of the senior management team could look to leave rather than face a potential reduction in their independence under sole News Corp ownership.
A senior insider said: "Under Jeremy [Darroch, Sky's chief executive], there is a really good, collegiate feel to the place with everyone working to drive shareholder value, and that is simply not going to happen in the same way with News Corp making all the decisions. There will be people who leave."
A major Sky investor added: "I think executives leaving is not just a possibility, it is an inevitability. Perhaps this won't happen immediately but it is clearly a very different ownership model."
While haggling over price, Sky and News Corp have agreed to co-operate on tackling the regulatory issues around the deal at Brussels and London, which could take a year to complete.
Last month, Sky reported an 11% increase in revenue to £5.9 billion in the three months to June 30, with operating profit up 10% year-on-year to £855m.