During their bidding war with Comcast, Disney suggested $38 per share in cash and stock for Fox's assets, which was approved by the Justice Department with the condition (that Fox agreed to), that Fox's regional sports networks are divested.
Fox said the performance of Sky since 2016 justified its new bid.
The speed with which Comcast's Brian Roberts returned with a higher offer was created to show how determined he is to buy the group which is present in 23 million homes across Europe.
Janedis laid out four possible scenarios: Comcast outbids Fox for Sky; Fox outbids Comcast and adheres to all conditions; Disney and Fox walk away and sell Comcast the remaining 40% stake in Sky; and Disney wins both Fox and Sky.
Disney secured conditional United States approval to buy the assets last month, giving it an edge over Comcast's bid. Comcast offered $65 billion and is getting ready for yet another bid for Fox.
Neither Comcast nor Sky immediately responded to requests for comment.
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Should Disney succeed, it will obtain Fox's 39 per cent stake in Sky as part of the package. Fox wants a deal at 14 pounds a share.
Fox's bid for Sky is the most recent episode in Murdoch's long-running effort to take full control of the company.
Now it's up to Comcast (cmcsa) to decide how much Sky is worth. According to some shareholders, that has set an implied higher floor for Sky's shares.
The Government had been concerned over the impact that Fox's takeover of Sky could have on United Kingdom media, given that the Murdoch family also owns News Corp - the publisher of a raft of newspapers including The Sun and The Times.
He said amended guarantees had been made over Sky News to address concerns over media plurality, as well as changes to the associated brand licensing agreement following responses to the Government's consultation.
The improved bid means Sky investors now have 60 days to weigh up the offers. The opposition has not completely subsided despite the plan to spin off Sky News.