Crispin Odey, founder of Odey Asset Management, told The Sunday Times that the pay-TV giant is worth £19bn, meaning that News Corp would have to pay £11.6bn for the 61% of shares that it does not already own.
A price at that level would be considerably higher than the £7.8bn, 700p-a-share offer submitted by News Corp last June, but turned down by Sky's independent directors.
Odey, who holds 2.3% of Sky, declared after the opening bid was submitted that any fair offer for the satellite broadcaster must be more than 900p per share.
Alongside Odey, the other major shareholders in Sky include investment firms BlackRock, Capital Research Global Investors, Franklin Templeton and Fidelity, along with insurance company Legal & General.
This week, culture secretary Jeremy Hunt is expected to give the final greenlight for News Corp to progress with its takeover of Sky, subject to a further seven-day consultation.
Should the approval go ahead as expected, News Corp would have two months to negotiate a price with Sky's independent directors and agree a deal.