Trapattoni left the role last month having failed to qualify for the 2014 World Cup, while interim boss Noel King took charge of Friday's 3-0 defeat to Germany and will also oversee tomorrow's final group clash against Kazakhstan.
"I want someone who is an honest manager who doesn't mess around, understands how important it is to be involved in international level, someone who is very, very proud to be a manager and be proud of what we are trying to achieve in Ireland," Keane is quoted as saying by PA.
"Someone who is honest and someone who has balls and doesn't take any shit from anyone. The names I have heard being mentioned, if any of them took over, I think everybody would be fairly happy. It could be any of those - I don't know the answer to that.
"I think it's important whoever takes over it's a fresh start for everybody, the whole country gets behind them and we wish them well whoever that may be."
Keane is in line to win his 130th international cap tomorrow having been passed fit following an ankle injury.