Parker said: "I'm looking forward to it. Sparring against the champ, there's only one thing that's going to happen and that is you're going to learn."
Duco and Barry believe Parker is ready for his next step up after easily overcoming Pettaway, who had been beaten only once in 18 fights, with a fourth round knockout in Manukau. Parker's record has gone to 13 victories, with 11 knockouts. He has yet to taste defeat as a professional.
"A bigger challenge is going to bring out the best in Joe," Barry said. "The [Francois] Botha fight was a big challenge at that stage. The [Brian] Minto fight for him was a big challenge, and then the fight at the end of the year [against Irineu Beato Costa Junior]. When he has really had to dig deep against quality opponents, that's when we've seen Joseph's best work."
Barry said Parker's next opponent was not likely to be a tall man.
"There's a lot of tall guys in the heavyweight division and those who aren't tall are very strong, powerful guys who come forward and are in your face the whole time. For us it's a no-brainer, either we go after one of the big tall guys which is not practical for me at the moment because we haven't worked with them in the training camps, or we go after someone who will put a lot of pressure on Joe and chase him down and try to beat him down."
Barry and Parker were slightly downcast following the victory over Pettaway at the Vodafone Events Centre, with the trainer saying it was a good, rather than great, performance.
Parker said he may have been trying to finish the fight, his first of the year, too early.