The Prime Minister said he considered taking Mr Minto and raised it with officials.
"In the end, the decision was made that the grouping we had was the right one. There are lots of potential names that were put into the pot. We think we've got it right."
Asked whether he personally wanted Mr Minto to go to South Africa, Mr Key said: "I wanted to raise and canvas a whole range of people and I did that."
Mr Key was also questioned about his stance on the 1981 Springbok tour. He has previously said he could not remember whether he was for or against the tour.
He told reporters this morning: "I'm not going to go and revisit that because if I do I'll spend all day talking about it and I can't be bothered."
He added: "As I've always said, I didn't go to protest against the tour and I didn't go to any of the games. I was 19 years of age and had lots of other things going on at the time.
"I'm strongly opposed to apartheid, but I'm not going to make up stuff that wasn't the case 30 years ago and try and reinvent history because it's inconvenient for the left."
Mandela, South Africa's former president and anti-apartheid hero, died on Friday after a lengthy illness.