The Gannett Foundation said yesterday that it rejected as "unsatisfactory" a $540 million offer by Gannett Co. to buy back the foundation's 10 percent stake in the Rosslyn-based media company.

The foundation, a charitable organization that is separate from Gannett Co. but is headed by former Gannett Co. chairman Allen H. Neuharth, said it would begin seeking offers from third parties for its stock. The foundation has been attempting to sell its Gannett Co. shares since April. Unsuccessful negotiations between the foundation and Gannett Co. over the stock sale have intensified a feud that apparently began developing after Neuharth retired as Gannett chairman in April of last year.

Sources close to the negotiations said the foundation has already had informal discussions with Paramount Communications Inc., Rupert Murdoch's News Corp., British press baron Robert Maxwell, Revlon Corp. Chairman Ronald Perelman, Texas financier Robert M. Bass and the leveraged buyout firm of Kohlberg Kravis Roberts & Co.

All these parties have been involved in controversial corporate takeovers during the 1980s, indicating that foundation officials are unconcerned that their 10 percent block could be used by a hostile suitor to launch a bid for the company Neuharth once ran. Financing for leveraged takeovers, however, has grown scarce.

The foundation would not comment on outside negotiations yesterday.

The foundation is seeking to sell its 15.9 million Gannett Co. shares, which make up most of its assets, to diversify into higher-yielding investments to satisfy federal tax requirements.

Gannett Co. officials reiterated that the company, publisher of USA Today and 83 daily newspapers, is interested in buying the stock at its current stock-market price. The stock closed yesterday at $32.87 1/2, up $2. Gannett's formal $540 million offer reflected the shares' closing price of $33.87 1/2 per share on Sept. 14. The foundation, however, has sought at least twice that amount, according to those familiar with the talks.