Trapattoni left his post by mutual consent on Tuesday after the team's 1-0 defeat to Austria in World Cup qualifying.
Kilbane now believes that McCarthy, who previously managed Ireland for six years until 2002, should be given a second spell in charge.
"I think Mick McCarthy would be perfect for the job," he told BBC Sport. "Martin O'Neill would raise morale if he was given the job. From knowing Mick and how he works, he'd be the one for me. Chris Hughton would also be a very good appointment."
Former Aston Villa manager O'Neill is the early favourite to replace Trapattoni.