Everton chairman Bill Kenwright claims he is confident star men Marouane Fellaini and Leighton Baines will stay at the Premier League club.
Belgium international Fellaini, who has a release clause in his contract, has been heavily linked with a move to Arsenal and has repeatedly stated his desire to play in the UEFA Champions League.
But Kenwright said in the Times: "I have to say he has given me every indication he doesn't want to go."
There has also been speculation that Baines, whose contract has two years to run, could link up with former Toffees boss David Moyes at Manchester United.
But asked whether the England full-back will be offered a new deal, Kenwright said: "Absolutely right. That's started; started in that he knows we want him to stay."
Should a club meet Everton's asking price a Fellaini sale would represent a substantial profit on the £15m club record fee they paid Standard Liege in 2008.
And though new boss Roberto Martinez would be loath to lose the Belgian at the start of his tenure, he can expect any funds to go back into his transfer pot.
"He talked about a couple of new signings and he talked about the squad and asked 'Do they need to go?'," said Kenwright of his discussions with Martinez.
"I said 'No, they absolutely do not have to go' (although) there is one (Fellaini) that has a get-out which everyone knows.
"I said to (Roberto) 'I can't sit here and give you a line because we all know money is everything in football - this is the money we've got and I will try to improve on it.
"We are desperate to find new owners and new investment but he will get support from everyone at the club and all the financial support - and by that I mean if he sells someone he won't get 80 per cent of that he'll get 100 per cent.
"Plus he has a certain amount of money for the transfer window which David was going to have."
Where will Marouane Fellaini start next season?