Martinez, who paid a record £13m fee for a Scottish player when he enticed McCarthy to follow him from Wigan in the summer, has been thrilled with the speed he has settled in at Goodison.
He told the Liverpool Echo: "Yes maybe one day (he can be captain). He already sets a great example.
"He embraces challenges and wants to help the team while also being humble. The way he's started has been a joy and he deserves the milestone he has achieved.
"Sometimes it's hard to go into the unknown but when James arrived here he had a solid background with the amount of games he'd played at a very young age."
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