London-born Rice, 19, is considering a turn to play for England who have won three favorable caps for the Republic.
McCarthy, in his next term as Republic of Ireland boss, met the midfielder earlier this season.
“He is the next captain, he is that kind of player,” McCarthy told Sky Sports.
“I had a really good meeting . It’s around him when he would like to decide. That’s the way I left it.
“It’s not my decision regarding if he plays for the Republic of Ireland. It’s only my job that if he would like to stick to us I really could pick him”
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Former Ipswich director McCarthy has returned to the Republic project in host to Martin O’Neill and he has put Rice a deadline of this opening Euro 20 20 qualifier against Gibraltar on 2-3 March to make a decision.
Rice declined to get involved in this Republic’s unsatisfactory Uefa Nations League effort while he believed that the possibility to play for England but recent press reports have indicated he has become prepared to dedicate to playing for McCarthy’s side.
“I’d love to build a team around him. We start in March. That’s my deadline because I want to know at the same time,” added McCarthy.
“He is the next captain, he is that kind of player. 100 caps would be a wonderful profile to have”
The Republic of Ireland will even face Switzerland, Denmark and Georgia in Group D of the Euro 20 20 qualifiers and McCarthy has also disclosed he is hoping to convince Leeds United striker Patrick Bamford to rethink his availability before the campaign begins.
“I have asked . I have inquired about a lot of players just such as I normally do. My intention is to talk with Patrick. I believe he will qualify. He is a very good goal scorer,” he also added.
Bamford, 25, reflected that the Republic at under-18 degree but played for England at the same age group and won two caps during England boss Gareth Southgate’s tenure because the under 21s director.