Parker is well aware of Meehan's power and his ability to go the distance, and Barry believes his young charge is ready to be tested, with some similarly big and powerful fighters looming ahead.
"We have a lot of big guys coming up for Joe to fight as he moves forward and keeps developing and maturing," said Barry.
"Kali's a big guy and it's the sort of the fight that three years into his professional career, is the right fight for Joseph to have now.
"You only have to look at the knockout percentages of Kali Meehan throughout his career and you know he punches like a heavyweight and he has a tremendous right hand that we have a lot of respect for.
"So it's a fight that Joe's got to follow the game plan. And everything he's shown me, I'm very positive that he will follow the game plan."
While Parker has been working hard to be ready for a long night in the office, he acknowledged both he and his opponent have the ability to end the bout quickly.
"We train for 12 rounds but the boxing game is funny and anything can happen," he said.
"One punch can change anything. We know that Kali's got power. I've got power, so it's just about who fights the smartest."
The 23-year-old shrugged off Meehan's recent comments that his son and training partner, Willis, packed a harder punch, saying it was just a part of the pre-fight hype.
"It's all part of the game. I'm sure Willis does have power because, of course, every heavyweight has power.
"It's a matter of landing the punches. I respect what he says, and that's his opinion, but after the fight we'll see if thinks I have power or not."