David Moyes is certain to return to his old side with an increased offer for Marouane Fellaini and Leighton Baines, according to The Telegraph.
It is believed that Manchester United had bid £28 million for the two players around 48 hours before the start of the Premier League.
Everton had decided to not make this information public so as not to effect the Toffees' start to the campaign.
''Everton can confirm that it has received bids from Manchester United for two players. Those bids were immediately rejected out of hand as derisory and insulting,'' said Everton's director of communications, Alan Myers.
''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 any way.''
The break-up is believed to be £16 million for Fellaini and £12 million for Baines, which doesn't meet the valuation for the players, according to Everton.
They had previously rejected a bid of the same amount from United from Baines, citing plainly that it was not enough.
As for Fellaini, Moyes had bought him from Standard Liège in 2008, which cost the club £17.5 million after various add-ons. A lesser bid for the Belgian, who has proved himself time and again in the league, is completely not justified.
The clause in his contract, which states that Everton are obliged to discuss a move away for the midfielder, if an amount of at least £23.5 million is bid, has also reportedly expired at the end of last month.
United have to bid a minimum of that amount, if they hope to prise Fellaini away from his club.
With Cesc Fabregas starting Barcelona's season opener, in which they comfortably routed Levante 7-0, hopes of signing him are declining with each passing day.
For Moyes, the priority remains to sign a central midfielder this summer, and he may well press for the Belgian after no substantial addition to the squad.
Coming back to Baines, a bid for him looked credible two months back, with Patrice Evra's unpredictability and Alexander Buttner's inexperience the only left-back options for Moyes.
But, Evra seems to have gained his old touch and United may dispense away with the search for a left-back.
But, even if United persist in their attempts to bring the English left-back, Everton shall not release him for a fee in the range of £12 million.
He is one of the best defenders currently in the Premier League, and Everton will hope to make maximum profit out of that deal.
If that happens, there is a likely chance that Evra may be released by United, possibly to his old club AS Monaco.
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