TalkSPORT reports how the Paris Saint Germain boss was identified by Sir Alex Ferguson as his first-choice successor, after the 71-year-old Scot announced his decision to retire at the end of the season.
However, Ancelotti politely declined the invitation to take over at Old Trafford, as the Italian holds out for another offer - from Real Madrid - to replace Jose Mourinho at the Santiago Bernabeu this summer.
Mourinho is expected to make a sensational return to the Premier League, to replace interim manager Rafa Benitez at Stamford Bridge.
Russian owner Roman Abramovich has held clear-the-air talks with the Portuguese tactician, and is ready to offer him the chance of a Chelsea comeback.
After Ancelotti rejected Manchester United's overtures, the newly crowned Premier League champions then turned their attention to second-choice Moyes, whom Ferguson had already held preliminary talks with about the managerial position.