The Manchester United legend says Roman Abramovich approached him to take over at Stamford Bridge in 2003, and has backed David Moyes to succeed after a tough start
The Scot called time on his Manchester United career in May after 26-and-a-half years at the Old Trafford helm having won 38 trophies with the club, including 13 Premier League titles.
And Sir Alex says he was approached to replace Claudio Ranieri at Stamford Bridge when Abramovich arrived in England, but the tentative offer was dismissed immediately.
"They used an agent to approach me when Abramovich first took over the club and I said no chance," Sir Alex said in an interview on American TV.
David Moyes - chosen by Sir Alex as his successor - has struggled in his new role, with United currently sitting 12th in the Premier League table with a return of just seven points from six games.
But the 71-year-old remains confident that Moyes is capable of achieving success at Old Trafford, and reaffirmed his decision to retire from the game.
"United are in good hands with David Moyes. He will be fine. He's a good manager," Sir Alex said.
"I'm not interested in managing again or getting myself worked up about Manchester United's results.
"You would be throwing your money down the drain if you put any money on me coming back as a manager. 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."