The Sunday Times, citing unnamed sources in London, said the decision to sell Volvo, which is part of Ford's Premier Automotive Group, was made in the past two weeks, but that the timing of the sale had yet to be decided.
No bank had been appointed to handle the transaction, the newspaper said, adding the deal could be worth $8 billion.
Ford spokesman Tom Hoyt on Sunday said the company wasn't commenting on speculation about Volvo's future.
Ford acquired Volvo from Sweden's Volvo AB in 1999 for $6.45 billion.
Last month, Ford said it was reviewing its position on Jaguar and Land Rover, fueling speculation that company was getting closer to selling the fellow Premier Automotive Group brands.
Ford sold Aston Martin, another part of the Premier Automotive Group, for $848 million in March, with some analysts saying the luxury brand did not fit into Ford's long-term survival plan. That plan includes cost savings by developing multiple models worldwide on the same underpinnings.
The possible sale of Volvo comes as the company is struggling to return to profitability in the face of fierce competition from Asian automakers and developing tastes for more fuel-efficient models in its key North American market. It is slashing thousands of jobs and plans to close plants to cut costs.
Dearborn, Mich.-based Ford posted a narrower loss of $282 million for the first quarter. The Premier Automotive Group reported a record pretax profit of $402 million for the quarter, due largely to Volvo.
And Ford has been relying on Volvo, an analyst has said, as it tries to globalize its engineering, design and manufacturing systems.