Hunt has been considering responses to a consultation on his decision to approve plans to spin off Sky News as an independent company to ease media plurality concerns about the takeover. The minister said that his final decision would be announced "just after" the return of parliament tomorrow.
Sky's share price has risen well above the 800p mark that its independent directors said last June they would at least consider a bid from Rupert Murdoch's media giant.
Last Thursday, Sky shares reached 843p, valuing the company at £14.8 billion, considerably more than the £12.3bn price tag when News Corp submitted its bid last year.
Industry figures contacted by the Financial Times believe that there will not be a legal challenge to Hunt's eventual approval of the takeover.
A group of rival media firms opposed to News Corp's action, including BT and the publishers of newspapers such as the Daily Telegraph and Daily Mail, are thought to have privately dismissed a judicial review of the decision.
Should Hunt give News Corp the greenlight this week, the move would be followed by Sky's first quarter profits statement on Thursday, in which the company is expected to post further growth in profits and customer numbers.
Speaking to PA, Nomura analyst Matthew Walker predicted that Sky will post a net addition of around 40,000 new customers over the three months, helping the firm's underlying profits to increase 15% to £252 million.
However, Hunt could also this week announce that he has accepted a number of criticisms about the Sky News remedy, and present an alternative remedy, potentially triggering a further period of consultation.
Critics of the plan have argued that the Sky News company would be wholly reliant on News Corp/Sky for its income and so would lack genuine independence.
A further complicating factor is the phone-hacking scandal involving the News Of The World, the tabloid paper operated by the News Corp-owned News International.
Rival groups have argued that Hunt should take the controversy into account, but the culture secretary's officials have said that he cannot link the two matters because the Sky takeover is being reviewed solely on media plurality grounds.