Cable provider Comcast Corp. (CMCSA) is not interested in raising its bid for Walt Disney Co. (DIS) to match the current stock price of the media conglomerate, a source close to the company said on Tuesday.

The move dampened expectations that Comcast may significantly raise its $48.8 billion bid for Disney.

Comcast is also leaning against running a shareholder consent solicitation to replace all or part of Disney's board while Disney's stock price continues to trade at these levels, the source said.

Disney rejected Comcast's unsolicited all-stock offer on Monday, noting the bid represented a 15 percent discount to its latest stock price.

Comcast responded by saying the bid was a full and generous offer.

Comcast's all-stock offer for Disney was initially valued at $26.47 a share when it was launched on Wednesday, but the value has declined as Comcast's share price has fallen.

Based on current stock prices, the bid values Disney at about $22.95 per share. Disney shares were up 10 cents at $27.02  on the New York Stock Exchange (search).

"We are not interested in Disney at the current price levels," the source told Reuters on Tuesday. "Obviously, if we're not interested in Disney at these prices, we're not going to run a consent solicitation."

Comcast, the nation's largest cable TV company, and Disney both could not be immediately reached for comment.

Disney said on Monday it would consider any "legitimate proposal" that created shareholder value, and backed embattled CEO Michael Eisner (search), noting the company's current structure and strategy would maximize shareholder value.

"The interests of Disney shareholders, which represent the fundamental priority of the board, would not be served by accepting any acquisition proposal that does not reflect fully Disney's intrinsic value and earnings prospects," the company said in a statement.

Disney is slated to hold its annual shareholder meeting in Philadelphia, where Comcast is headquartered, on March 3. The Disney family, led by former director Roy Disney, is spearheading a campaign to oust Eisner.

Comcast, which owns a small stake in Disney, is not participating in the Disney meeting and is not expected to lead any shareholder campaign against Eisner that day, the source close to the company said.

"This has never been about Mr. Eisner," the source said, noting that most of Comcast's senior management would be at a long-planned management conference that day. "It has been about maximizing value for the shareholders for both companies."