"The Club did not make public these details as it was vital (manager) Roberto Martinez's preparations for the opening game of the Premier League season were not disrupted in any way."
The statement came after several media outlets in the UK, including the BBC, reported that former Everton manager David Moyes had lodged a £28 million ($44 million, 33 million euros) bid to bring the pair to Old Trafford, including £16 million for Fellaini.
A £23.5 million release clause in Fellaini's contract expired at the end of July.
The Premier League champions are believed to have offered the same amount for 28-year-old Baines -- £12 million -- that they bid in June when the offer was flatly rejected.
Everton claim Moyes made an unwritten pact with the club not to try to sign their players when he left in the summer to succeed Alex Ferguson.
Moyes signed both players for Everton, paying Wigan £6 million for Baines in August 2007 and signing the lanky Fellaini for a then club record £15 million from Belgian club Standard Liege in September 2008.
Moyes has been frustrated in the transfer market with attempts to bring Barcelona midfielder Cesc Fabregas to United so far proving unsuccessful, while England striker Wayne Rooney appears to want to leave Old Trafford for Chelsea.
United crushed Swansea 4-1 in their opening match of the Premier League season on Saturday, while Baines and Fellaini both played as Everton drew 2-2 with Norwich.