The bid represents the second time United have attempted to sign Baines this summer, with Toffees chairman Bill Kenwright confirming an offer was rejected out of hand, while Fellaini's release clause, thought to be in the region of £24m expired on 31 July.
Manager Roberto Martinez said United's bid for Baines was expected to be their final attempt to sign the England international left-back however a second bid suggests former boss David Moyes, who signed the pair from Standard Liege and Wigan Athletic during his 11-year spell in charge, doesn't intend to give up on the 28 year old.
"The Club did not make public these details as it was vital Roberto Martinez's preparations for the opening game of the Premier League season were not disrupted in anyway."
Both Baines and Fellaini were involved in Everton's Premier League opener against Norwich City and Martinez was planning for the new season in the belief the pair would remain on Merseyside this summer.
During over a decade at Everton Moyes consistently launched a staunch defence when his big-name players were subject of interest from rivals clubs however having signed both Baines and Fellaini and worked with them as recently as last season the Scot will be only too aware of their valuation.
And while that gives Moyes inside knowledge in pursuit of the duo it is likely to deter him from paying over the odds for players who cost £15m and £6m respectively.
Since officially taking over from Sir Alex Ferguson as manager at Old Trafford, Moyes' primary concern has regarded the future of striker Wayne Rooney, who reportedly wants to leave United after being marginalised in the first team.
After mysterious hamstring and shoulder problems restricted him to a behind-closed-doors friendly appearance against Real Betis during pre-season, Rooney was used only as a second half substitute for United in the 4-1 opening day win at Swansea City.
Rooney set up both second half goals for Robin van Persie and Danny Welbeck but notably refused to celebrate with team-mates - an indication over his unhappiness at the Premier League champions.
Moyes has been unable to make any significant additions in the summer transfer window since taking the reins at United, failing in two bids for Barcelona midfielder Cesc Fabregas.
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