The 26-year-old midfielder has been linked with a move away from Goodison Park in January after managing just five Premier League games under Ronald Koeman.
Celtic were linked with the Republic of Ireland ace during the summer but he ultimately ended up staying at Everton, though his situation hasn't improved.
And although The Record claims that Hoops boss Brendan Rodgers is still keen, the Scottish outlet reports that wage demands, coupled with what the Toffees would want for him, could price the Northern out of a move for him.
Signing McCarthy in January is not an urgent matter. With Scott Brown and Tom Rogic, Celtic have enough quality in centre midfield to do them this season, but the Scotland-born star could be a good long-term option to have.
Brown will turn 32 in the summer, while Rogic has been in excellent form this season and few would doubt that he will not get a chance to shine in the Premier League.
McCarthy could be a fine asset to have. He has proven himself a very tidy footballer in England's top tier which should, in theory, mean that he is well equipped for action in the Scottish Premiership.