The Evening Herald reports that United's offer values Fellaini at less than the £23.5m release clause that expired in July, but sources close to Old Trafford say they have set a £20m ceiling for the 25-year-old and there is no room for manoeuvre.
The belief is that Fellaini, for all his talents, is worth no more than £20M to United.
United are hard pushed on Baines too, that a 28 year old full back would be commanding a fee of £15M
Everton manager Roberto Martinez has publicly stated his desire to keep both players at Goodison Park, but the Spaniard wants the situation resolved quickly so that he can re-invest in the squad before the close of the transfer window.
Moyes is a huge fan of Fellaini and Baines, having worked with them at Everton before replacing Alex Ferguson at Old Trafford at the end of last season, and the feeling from the two players is said to be reciprocal.
The Red Devils allegedly will be prepared to progress with a separate deal for Baines should the Goodison outfit reject United's final bid for Fellaini.
Why this would be when it seems that United do need a midfielder far more than they need a left full back is beyond the man-on-the-street.
Moyes says he knows Everton inside out, and that he bought all the players there and he believes that Everton need the money from the sale of at least one of their star players this summer, with the Merseyside club lining up a double bid for Wigan's Irish midfielder James McCarthy and winger Callum McManaman.