Toffees boss Roberto Martinez is hoping to reunite with the highly promising Irish midfielder but his initial bid of around £7million, plus add-ons, was turned down.
It is believed that Wigan want £10m up front but even so, chairman Dave Whelan suggests McCarthy is happy with the Championship club.
"We have had a couple of offers for James McCarthy which we do not believe are good enough at the moment," he told the Daily Telegraph.
"We have a valuation on the player and until a club meets the asking price we will not be doing business, it's as simple as that.
"I have made a promise to James that he can leave if Wigan receive the right offer but we haven't received that yet. A few clubs have made inquiries but Everton are the first club to put some money on the table.
"James is perfectly happy at Wigan and if he stays beyond the deadline, then great. But this is unsettling for us as a club and the transfer window is barmy - it should shut at midnight the day before the season starts so we can avoid all this worrying."