Moyes expects Rooney to sign soon
Talks are planned on his new contract before Everton jet off to the United States at the weekend for a two-match trip to Houston, Texas.
Moyes said of the offer to Rooney: "Of course, I am optimistic. I said we are going to be positive at Everton and I am. We have made him a tremendous offer and I would expect that to be accepted.
"I think we have made a good offer and I am sure in the coming days or weeks we will find out exactly what is going on."
Even Rooney's camp are claiming the player is "confused and concerned" by the state he finds his beloved club in and a source said: "There is a large part of his heart still at Everton and he would love to stay."
Rooney is also believed to be upset by banners waved by Everton fans at Crewe on Tuesday which read: "What has happened to 'once a blue always a blue' Rooney."
Whether Rooney's love for the club will stretch to him signing a new deal he still has two years left of his current contract - remains to be seen given Everton's financial crisis.
Rooney's advisers are playing down the claims that a decision on the offered five-year contract, worth £50,000 a week, will be made in a matter of days.
Rooney's agents have changed their name to the Formation Group this week, and an insider insists "no deadline has been put on the contract discussions, which are ongoing."
What clearly concerns the Rooney camp is the chaos at Goodison Park, where two chief executives and two directors have left this summer.
Rooney's agent Paul Stretford had a meeting with Trevor Birch last Thursday and the following day the former Chelsea and Leeds chief executive was clearing his desk, to the amazement of the Rooney camp.
Those advisers a week earlier had presented Everton with a list of questions about the future financial viability of the club and its ability to deliver the deal offered to Rooney. They are still waiting for answers.
The boardroom infighting now sees chairman Bill Kenwright seemingly at loggerheads with director Paul Gregg, but with the backing of the only other director left, Jon Woods.
The saga seems to be disrupting Moyes' pre-season build-up and he had to watch his side lose 2-1 at Crewe in a friendly on Tuesday, while angry Everton fans voiced their fury at the state of the club.
The backdrop to the Rooney saga is the boardroom war between Gregg and Kenwright. Gregg has turned the screw by claiming he has financial backing that could bring in £15m if Kenwright agrees to a change the club's constitution to eliminate True Blue Holdings, which effectively runs Everton. "New investment is realistic, but without change it will not be available. It is as simple as that."




