The approach, which was lodged last week and values Sky at around £12 billion, was rebuffed by the independent director as working to "undervalue significantly" the Sky business. News Corp already owns 39% of the broadcaster.
In March, Sky shares soared to a 52-week high amid talk that News Corp was planning a takeover.
A formal proposal has now materialised, but the independent directors, under advice from Morgan Stanley and UBS Investments, feel that the 700 pence per share cash offer is too low.
However, the directors did indicate that they "would have been prepared" to accept an approach of "in excess of 800 pence per share" from News Corp.
Any takeover would be dependent on the companies satisfying regulatory conditions, specifically in terms of getting merger clearance.
Despite the tough economic conditions, Sky has been able to prosper in the digital TV industry and is on-track to pass the significant 10 million subscribers mark.
The company will be able to offer five out of the six packs of valuable Premier League rights from next season and is also bringing on new services, such as 3D TV and Anytime+ video on-demand.
News Corp, which is being advised by Deutsche Bank and JP Morgan Cazenove, reportedly intends to fund the deal with its cash reserves. The company believes that a full acquisition of Sky wil increase its global presence and reduce its reliance on advertising revenues.
Commenting on the proposal, Sky's senior independent non-executive director Nicholas Ferguson said: "The eight Independent directors have evaluated the proposal since receiving News Corporation's approach on June 10.
"Based on careful review and advice, it is the unanimous view of the Independent directors that there is a significant gap between the proposal from News Corporation and the value of the company. We believe the company has a track record of very strong performance and excellent growth prospects.
"The management team will remain fully focused on its strategic and operational priorities, positioning the company well to grow earnings and cash and increase returns for shareholders. The independent directors remain fully committed to acting in the interests of all shareholders and will continue to meet on a regular basis."
The Sky board has now set up a dedicated committee comprising of independent directors and executive directors who will have the "authority to exercise all powers of the board in relation to the possible offer and any matters relevant to the proposal".
Following the takeover proposal developments, Sky share price increased by 21% in early trading to 726.5p.