Veteran Ferguson has been in charge of the Red Devils since 1986 and has gone on to become the most successful manager in the club's history.
While the 70-year-old has refused to publicly reveal when he is planning to step down from his position, it has been speculated that he is considering calling time on his career at the end of next season.
Reports earlier this year claimed that Ferguson met with Guardiola, who is in the middle of a 12-month sabbatical from football, in New York to discuss the job and was left impressed by the 41-year-old.
Since that meeting, United chief executive David Gill and a member of the Glazer family have held further talks with the Spanish coach, according to ESPN.
Guardiola won 14 major trophies during his four-year stint with Barcelona, which ended at the end of the last campaign.