The Everton duo were the subject of a joint bid from Manchester United, reported to be in the region of £28 million pounds, which was rejected immediately by the club
New Red Devils boss David Moyes has expressed his interest in signing the pair from his former club, and last week Goal revealed Roberto Martinez is resigned to losing Fellaini this summer.
But the Spaniard retains hope of keeping Baines and getting a good price for the Belgian, whose £23.5 million buy-out clause expired on July 31.
A statement on the club's website read: "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.
"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 Fellaini and Baines featured in Everton's 2-2 draw with Norwich on Saturday, and it is thought United will have to significantly increase their latest offer, thought to be in the region of £28m, to secure a deal.
The Merseyside outfit are well known for their tough stance on transfer fees when selling players, notably under Moyes when they forced Manchester City to pay £22 million for Joleon Lescott.