The Red Devils' asking price is said to be around the £20 million, which, if true, would almost certainly put paid to Sunderland's chances.
The report claims that Moyes is restricted by the Black Cats' January budget, with relegation to the Championship a strong possibility as things stand.
Were Sunderland to remain in the Premier League, however, the Scot's chances of a third Fellaini link-up would perhaps be greater as the 29-year-old enters the final 12 months of his deal.
The pair enjoyed a successful working relationship at Everton, prompting Moyes to make the former Standard Liege player his first major signing at Old Trafford.
Will Moyes ever get Fellaini to the Stadium of Light?