The two young talents played in conjunction for Accies until McCarthy joined Wigan last summer. The Republic of Ireland international has since impressed for the relegation-threatened side.
With McCarthy adapting well to Premier League football, Martinez is retaining an interest in McArthur, who at the age of 22 is one of the brightest prospects in the SPL at present.
"James McArthur is a great talent," Martinez said. "What he has achieved at Hamilton in the SPL is remarkable.
"James McArthur is another player that we have been following for a long time. But, like him, we have a lot of names. It's nothing else than speculation.
"I am sure there are going to be a lot of names between now and the end of the season. 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."