Chairman Bill Kenwright remains hopeful key duo Steven Pienaar and Mikel Arteta will start the new season at Everton.
Both players, who are key members of David Moyes' squad, have been the subject of speculation over their futures throughout the summer.
South Africa international Pienaar, who is now entering the final year of his contract, is yet to commit to a new deal while attempts are also being made to negotiate fresh terms with Arteta.
Kenwright believes the duo are at one of the Premier League's best clubs and believes they would be making a mistake if they thought the grass was greener elsewhere.
Speaking at a shareholders' forum on Wednesday evening, he said: "I can't stand here and say this is going to happen but I remain hopeful.
"It is huge, the pull of the blue. I hope they say to themselves, 'Is there anywhere better than this?'
"I am more than hopeful we will start the season with players we want to start the season with."
Moyes made the re-signing of star players his top priority over the summer.
Tim Cahill, Jack Rodwell, Leighton Baines and Seamus Coleman all committed to new long-term deals.
Moyes feels he has a squad capable of competing with the best of the Premier League and is anxious to keep it together, but accepts money is an issue.
The Scot said: "We have the value on the field. We may not have it in the bank but we have it on the field.
"We have to make sure we keep the ones we have got, but wages will have to increase."
The one major negative for Everton during the summer has been the loss of promising youngster Dan Gosling to Newcastle on a free transfer.
The club's failure to make the 20-year-old a written offer of a new contract before a May deadline allowed him to move without Newcastle having to pay compensation.
When pressed on the matter, Kenwright reiterated his stance that the club had been let down.
Everton claim they had been given verbal assurances by Gosling's agent throughout contract talks that a new deal would be agreed.
Kenwright said: "If you can't rely on someone's word and handshake in this world, then we live in a world I don't want to live in."