The United manager tried to sign Moura in the summer, but the 20-year-old eventually opted to join Paris St Germain in a £35m deal.
And the report claims Ferguson was prepared to sell Nani, and had identified Moura as the ideal replacement before he spurned United's advances.
The Old Trafford boss has become increasingly frustrated with Nani, and criticised the Portuguese winger for his carelessness in possession during United's 5-4 defeat to Chelsea in the Capital One Cup last month.
The ESPN report also suggests Nani has become disillusioned with life at Old Trafford, and feels "victimised" by his manager who he feels blames him for any poor result.
According to the report, Nani's relationship with the United hierarchy reached breaking point after the Chelsea match, as Ferguson's assistant Mike Phelan had to act as peacemaker while Nani rowed with first-team coach Rene Meulensteen.
United were reportedly prepared to sell Nani during the last transfer window, but Moura's decision to join PSG instead of United prompted Ferguson to retain the Portuguese winger's services.
Manchester United have plenty of options in wide areas, with Nani jockeying for position with Ashley Young, Antonio Valencia and Danny Welbeck.
Moura is set to join PSG in January, after finishing the Brazilian season, and recently denied money was the main motivation behind his move to the French capital.