Martinez signed McArthur's former team-mate McCarthy last close-season and the 19-year-old has recently established himself in the first team.
"James McArthur is another player that we have been following for a long time," said Martinez earlier in the week.
"But, like him, we have a lot of names. It's nothing else than speculation."
Wigan are just above the English Premier League's relegation zone, but Martinez is already planning for a stay in England's top flight.
"I am sure there are going to be a lot of names between now and the end of the season," he said.
"As we did in the previous window, we follow a lot of names and a lot of players - it's about getting the right players and the right characters."
However, Martinez could be persuaded to return to Hamilton after seeing McCarthy adapt quickly to the rigours of English football since his £1.2m-plus transfer, despite still being in his teens.
The Glasgow-born midfielder has become a regular in Wigan's first team since the turn of the year and won his first cap for the Republic of Ireland.
James McArthur is a great talent. What he has achieved at Hamilton in the SPL is remarkable
Wigan manager Roberto Martinez
And Martinez admitted being impressed with Scotland Under-21 international McArthur, who has made more than 180 appearances for Hamilton during which he and McCarthy helped Accies win the Division One title and then establish themselves in the Scottish Premier League.
"James McArthur is a great talent," said the Wigan manager of the player who has been previously linked with a number of English clubs.
"What he has achieved at Hamilton in the SPL is remarkable."
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