Speaking to The Sun, the broadcaster joked that Morgan "actually rang to ask [his] permission".
"I talked a lot about it," Frost said. "We talked about the kind of people he wanted."
Frost also praised Morgan, saying: "It would be good if the show takes off. He is a good interviewer."
Piers Morgan Tonight airs on weeknights at 9pm ET on CNN in the US and at 8pm on CNN International in the UK.