Eriksson confirms in his new autobiography he was approached to take over from Ferguson as far back as 2002, four years before a bitter row ensued over Wayne Rooney's inclusion in England's World Cup squad.
Rooney was eventually passed fit for the tournament after recovering from a broken metatarsal, but he failed to score a goal and was sent off for stamping on Ricardo Carvalho in the quarter-final clash with Portugal which England lost on penalties.
Eriksson wrote: "Leif (Sward, England doctor) and I met Ferguson and United's doctor at the United training ground. 'He cannot play in the World Cup', Ferguson said flatly. The doctor brought out some X-rays that he said showed Rooney's broken bone would not heal in time.
"When the doctor finished, Leif looked him in the eye. 'Why do you sit here and lie to me?' Leif asked.
"He was one of Europe's foremost specialists on this kind of injury. I just wish I could have filmed Ferguson's face when Leif explained that Wayne's break would heal in time for the World Cup.
"When Leif had finished, I turned to Ferguson. 'Sorry, Alex,' I said. 'I will pick Rooney'."
Ferguson, who eventually retired at the end of the 2012-13 season, previously announced his intention to stand down in 2002, only 12 months after Eriksson took over the England job.
"I knew it would be tricky. I had a contract with England until the 2006 World Cup and I would be severely criticised if I broke that contract," Eriksson wrote.
"But this was an opportunity to manage Manchester United, probably the biggest club in the world. A contract was signed - I was United's new manager.
"I would be able to stay with England through the World Cup. My appointment would not be made official until after the tournament.
"A couple of weeks passed and Pini (Zahavi, Eriksson's agent) called again. He wanted another meeting. When I got there, I knew something was wrong. (Peter) Kenyon explained Ferguson had changed his mind.
"He did not want to leave the club after all but had agreed to stay in the job for another three years."