Toffees boss Roberto Martinez has been chasing a reunion with McCarthy in recent weeks, with Wigan confirming that Everton lodged an offer earlier this afternoon.
Whelan has revealed that Everton offered to pay for McCarthy in instalments which would see full payment take four years, terms he would not even consider.
He told BBC Sport: "Everton are not matching what we are looking for. We asked for a certain price from Everton for James McCarthy, and they have not come near it.
"We have to be fair with the player, and our football club. They said they were going to pay us over four years.
"We did not make an offer for Jordan Rhodes. We would not do that until we sold James McCarthy."
Wigan's valuation of McCarthy is thought to be at around the £14m mark, with Everton now facing a race against time to conclude their business before the transfer window closes at 11pm.