"He had to answer those questions, but straight after that I said 'I don't want to hear Anthony Joshua's name mentioned for the rest of this training camp. The only person I want you concentrating on is Solomon Haumono'.
"We have a very big target on our back now. A lot of people want what Joe has. I've been in this game a long time now and I've seen a lot of guys look past the man in front of them at the big prize and come unstuck."
Parker and his team have arrived from their Las Vegas base in good spirits following a five-week camp. Parker had some time off following his 12-rounder against Carlos Takam which earned him his precious title shot against Joshua, a fight won by unanimous decision which challenged him like none before, but said an intensive camp with quality sparring has him in good shape for Haumono.
The three-month Takam camp, and tough fight, took a lot out of him and exacerbated a left elbow problem which Parker and his team have been managing carefully.
"The body adapts better to the shorter camps," he said. "During the 12-week camp there were a few weeks there when the body hit the wall ... we were lucky to be able to build back up to the fight in time, but for this fight I feel in great shape.
"It would be nice to stop him, but Solomon has been taking this fight very seriously,"
Parker said when asked if he would like a knockout victory.
"He's taken his whole training camp to LA and he's training with Manny [Pacquiao's] conditioning trainer Justin Fortune. For him this is make or break, he wants what I have, the mandatory position to fight for the IBF world title. What I'd like to see for myself in this fight is better defence, better movement, better distance. I'm a taller man so I should be using what I have to my advantage."
Asked about the 26-year-old unmentionable, and when he might face him for the title, Parker said: "I'd like to face him when they're ready. He called us out after the [Breazeale] fight and I think our team has approached him and asked his team to take us any time they're ready. I think they want another fight but we're ready any time.
Barry said: "He and his promoter are in charge of that decision. There's a chance we might fight him in November. Personally, I don't think it's an option they want to take. All I know is, when we fight him in November or March, April next year, when that time comes we'll be ready to step into the ring. When the lights are on that's when Joseph shines the best... the bigger the fight the bigger Joe's game."