Ferguson has yet to give a definitive answer about when he intends to retire, but does expect it to be sometime within the next three years.
Giggs, meanwhile, extended his stay at Old Trafford for a 22nd season earlier this week by signing a one-year contract extension and is about to make his 900th appearance for the history rich club.
The 38-year-old has maintained an excellent relationship with Ferguson for the duration of his time with the club and, according to the Daily Mail, the United boss has told friends Giggs has the right credentials to replace him.
Jose Mourinho and Pep Guardiola have been mentioned among other potential successors, but it would appear Giggs could be the leading candidate for the role.
And Paul Scholes, speaking to FourFourTwo magazine earlier this month, also backed the Welsh legend to take the Old Trafford hot-seat.
"People have talked about Jose Mourinho. It can change quickly - it's about who is successful at the time," he said.
"Whether they are British or foreign, you just want the best man for the job. I could see Ryan Giggs becoming manager."