Ferguson, speaking to Charlie Rose on American network PBS, claimed that he had been contacted by an intermediary acting on behalf of the Chelsea owner.
However, Ferguson rejected Abramovich's overtures and Chelsea kept hold of Claudio Ranieri until the era-defining appointment of Jose Mourinho in 2004.
“They used an agent to approach me when Abramovich first took over the club,” Ferguson said.
“I said, 'No chance,'” he continued.
Ferguson was always going to be a tough act to follow having won an incredible 49 trophies in his 26-year tenure at Old Trafford but he was adamant that he would not be tempted out of retirement regardless of how successor David Moyes performs.
The former Everton boss has lost three of his first eight games in charge of the club.
“I’m not interested in managing again or getting myself worked up about Manchester United’s results,” Ferguson said.
“I made my decision. The timing was perfect. There is no way back for me now. I’ve got a new life.
"I want to go to the Kentucky Derby and the US Masters, the Melbourne Cup. I want to visit vineyards in Tuscany and France."
Bookmakers have slashed the odds of Ferguson returning to the Old Trafford hot-seat if Moyes’s woes continue but he was keen to praise the credentials of his successor - despite the Red Devils making their worst start to a league season in 24 years.
“United are in good hands with David Moyes. He will be fine. He’s a good manager.
“You would be throwing your money down the drain if you put any money on me coming back as a manager."
Ferguson confirmed that Rooney did indeed ask to leave after the Premier League title was secured at the end of last season, but added that he has been impressed with how the England striker has worked on his game in recent weeks.
He also revealed the key to his the famous 'Fergie time' goals - the late equalisers and winners which often characterised his teams' performances:
"I always say to them at half-time, in the last 15 minutes - throw the kitchen sink!"