Everton would not give details of the offer, which has been passed on to the 18-year-old's agent amid speculation that Rooney's sparkling performances at Euro 2004 could trigger a move to a bigger club. Chief executive Trevor Birch told the club's website on Tuesday: "We believe this is the right offer for Wayne - one which fully reflects his growing stature within football.
"The five-year deal which has been offered to Wayne is the biggest ever made in this club's history and will hopefully not only satisfy Wayne's demands but will also serve
He added: "Everyone at Everton is anxious that Wayne remains at Goodison Park to continue his footballing education under the stewardship of David Moyes and his coaching staff."
Liverpool born and bred, Rooney has come up through Everton's youth ranks since he was nine.
His meteoric rise over the past two years was topped off by scoring four times in England's Euro 2004 campaign in Portugal before breaking a bone in his foot in the early stages of their quarter-final defeat by the host nation.
Rooney has two years left on his current contract, signed in January 2003.