The Red Devils have made two attempts to sign Barcelona midfielder Cesc Fabregas so far this summer, but on both occasions their advances were knocked back by the Catalan giants.
As a result, manager David Moyes has turned to his former club Everton for Belgium international Fellaini to boost his midfield options, according to the London Evening Standard.
The report added that Moyes is also keen to recruit left-back Baines, who is believed to have been the subject of a £12m bid from United back in June. Everton rejected that offer and are thought to want around £18m for the England international.
While no other official offers have been made, United are reported to be confident that they secure a deal for both players before the end of the ongoing transfer window.