Manchester United manager David Moyes is trying to sign Marouane Fellaini and Leighton Baines from Everton but his former club has rejected the approach.
After reports of a joint bid of 28 million pounds ($43 million) for the players, Everton said it had "been rejected out of hand."
The club said the offer was "derisory and insulting."
Moyes signed Fellaini for Everton in 2008 for a fee that has already reached 17 million pounds ($27 million). The 25-year-old Belgium midfielder's Goodison Park contract runs for another three years.
Baines, the 28-year-old England defender who joined Everton for 6 million pounds ($9.4 million) from Wigan in 2007, is under contract until 2015.
Moyes moved from Everton to United in the close season after Alex Ferguson retired.