While Toyota's U.S. sales have jumped by almost 13% this year, Ford's have fallen by almost 8%.
The Nihon Keizai said Toyota could be considering a partnership as a way to ease potential friction with the U.S. auto industry at a time when its own growth -- as well as exports from Japan -- has been surging.
"As part of its strategy, Toyota is sweeping across the U.S. market. This could be a countermeasure to avert potential criticism," said Katsuhiko Kodama, senior strategist at Toyo Securities.
Mulally, who took over as Ford CEO in October with a mandate to turn the struggling company around, has spoken repeatedly about his admiration for Toyota, a company he said he studied closely as a manufacturing executive at Boeing.
Ford currently licenses part of Toyota's market-leading hybrid engine technology for the gasoline-electric versions of its Escape and Mariner sport utility vehicles.
Ford, which has relied heavily on its line-up of trucks and SUVs, would stand to gain from a cooperative partnership with Toyota if it focused on fuel economy and other technology seen as environmentally friendly, said Edmunds.com analyst Jesse Toprak.
"In terms of long-term planning, I think it's very smart for Ford to be looking at this," Toprak said. "This is going to be a factor that will determine whether an auto maker is successful in the future."
Efraim Levy, an equity analyst at Standard & Poor's, agreed.
"Toyota could teach Ford a lot in any kind of joint venture (such as) suggestions on improving manufacturing efficiencies or sharing technologies," he said. "The benefits that would accrue to Toyota are less obvious."
He added: "I don't think any major transaction is going to occur between them. It's probably just going to be technology sharing."
The possible partnership is the latest of several that have captured headlines for the global auto industry in recent months.
GM declined to enter an alliance with Nissan-Renault in early October after three months of talks, triggering speculation the French-Japanese auto group could turn to Ford to secure a North American partner.
Carlos Ghosn, who heads both Renault SA and Nissan Motor Co. , said last month he was open to adding a U.S. automaker to form a three-way alliance, but said the timing was not right for Nissan.