According to reports last week, McCarthy had been linked with the vacant Republic or Ireland manager role but Tunnicliffe thinks it's important for Ipswich that he remains at the club.
Tunnicliffe said: "It would be a big blow if he were to go. The fans, and the players especially, don't want him to go.
"I have travelled in a few squads with Sir Alex Ferguson so it is hard to compare the manager here with the greatest ever manager, but they both have the same fiery temperament and determination to win."
The 20-year-old midfielder impressed during Ipswich's 3-1 win over Middlesbrough at the weekend and said that McCarthy was always in control even when they fell behind early on.
Tunnicliffe added: "Mick was calm and just pointed out where we could do better.
"He is not one to shout and bawl and was just focusing on what we were doing well - no hairdriers."