The Latics owner said that the bid - believed to be in the region of £10m - was turned down because it did not meet their valuation.
"We rejected the bid because it's still not near the value we'd expect," BBC Sport quotes Whelan as saying.
"If we have to sell James, then we will have to bring someone in and that's not easy. I really hope he stays with us. Everyone seems to leave the business until the last minute."
Everton manager Roberto Martinez, who joined the club from Wigan over the summer, is said to be lining up McCarthy as a potential replacement for Marouane Fellaini amid reports that the Belgian is bound for Manchester United.