In a wide-ranging hour-long interview with US TV network PBS, Ferguson, who left United in the summer after almost 27 years in charge, revealed he was asked to manage Chelsea not long after Russian Roman Abramovich bought the club in 2003.
"They used an agent to approach me when Abramovich first took over the club," the Scot said.
"And I said, 'No chance'. I always come back to this point - why would you leave?"
Harris wondered why Ferguson chose now, after successor David Moyes' challenging start at Old Trafford, to reveal the approach.
"Why bring it out now?" Harris told Press Association Sport.
"They haven't started the season off particularly well. Maybe he's trying to upset the apple cart.
"If it was true, I'd have thought it would've leaked out before.
"It just seems strange now all of a sudden since he's retired it's come to light."
It is the first time Ferguson has commented publicly on the matter, although it was previously reported by the Manchester Evening News.
It was not a shock to Chelsea Supporters' Group chair Trizia Fiorellino.
"I'm not surprised at all; I'd have been surprised if he wasn't offered the job," she said.
"Abramovich was very new to football and was going around trying to pick up the best of people to fill the football club with."
Fiorellino wonders whether Ferguson and Abramovich would have got on.
She added: "Ferguson was very well established at Man United at the time and coming to Chelsea, where there's talk of Abramovich interfering, how long would that relationship have lasted?
"I don't think Ferguson would've put up with any interference whatsoever."
Had Ferguson been appointed, Jose Mourinho might never have become the most successful manager in Chelsea's history. The Portuguese is now in charge for a second spell.
Fiorellino added: "Everything works out for a reason and if Fergie turning us down brought us Jose eventually, it was meant to be.
"It's part of the Jose Mourinho and Chelsea fairy story."