The Ford family controls almost 40% of the voting power at the automaker through a separate class of shares established when the company went public in 1956.
The family's stake of almost 71 million Class B shares represents only about 4% of Ford shares outstanding, but each family share carries 16 votes compared to the single vote for each share of common stock.
"The Ford family is not discussing the sale of its holdings in Ford Motor Company," said Ford family attorney David Hempstead, on behalf of the family. "Statements attributable to unnamed sources are untrue."
A person familiar with the matter who asked not to be named told Reuters on Monday the Ford family had met with representatives of an investment bank last month, but it has not retained any firm to advise it on its controlling stake in the automaker.
Ford has been cutting jobs and closing factories to turn itself around as it loses market share to foreign competitors.
Earlier in May it said that 25,000 factory workers had left its payroll after taking buyouts, and it said it would close a Cleveland casting plant and idle a nearby engine plant for a year.
The company posted a record loss of $12.7 billion in 2006 and another $282 million loss in the first quarter.
Ford shares rose on Monday, at one point gaining 4.8%, their biggest percentage increase in more than six months.
The gains were sparked partly by a Bloomberg report that founding family members were weighing the sale of a part of their controlling stake in Ford, said Kevin Tynan, an analyst with Argus Research.
The proposed sale of competitor Chrysler Group to Cerberus Capital Management also raised expectations of a faster and broader restructuring for the U.S. auto industry, sparking gains for both Ford and General Motors, analysts at JP Morgan and Bear Stearns said in notes. GM shares were up 3.5% at $30.49 in late afternoon trading on the New York Stock Exchange.
Tynan said that a dilution of the Ford family's holdings in the company could be positive for shareholders.
"If they also wind up with a private equity deal, it gives shareholders a little flexibility, which has been difficult because of the controlling stake of the family," Tynan said. "It's been very difficult to implement any change."
The Detroit News reported last week that some members of the Ford family met with Wall Street firm Perella Weinberg on April 21. The principals of that firm have a track record of arranging corporate mergers and acquisitions.
The newspaper reported that Steven Hamp, brother-in-law to Ford's Executive Chairman Bill Ford Jr. and his former chief of staff, said the possibility of selling the Ford family's interest in the company did not come up at that meeting.
A Ford spokesman on Monday confirmed Hamp's statement. A proposal to eliminate Ford's Class B shares was voted down at Ford's annual meeting last week with 27% of votes cast in favor of the proposal which had been opposed by the Ford board.
Bill Ford Jr., the great-grandson of founder Henry Ford, has repeatedly defended the dual stock structure as a benefit to shareholders.
Ford Chief Executive Alan Mulally told reporters after the shareholder meeting in Delaware last Thursday that Ford family members were "very, very supportive of the changes" the auto maker has been making. "They are shareholders; they believe in Ford and want Ford to be successful," he said.