Parker's last two bouts have gone the distance -- his win over Andy Ruiz Jr late last year which earned him the WBO belt, and his first defence against Razvan Cojanu in May.
A knockout victory in the current home of heavyweight boxing would announce the 25-year-old as a bankable force to be reckoned with.
"We're going really hard on this fight," Barry added. "We want to make an impression, we want to make a statement.
"I believe after this fight people will be talking about the power of Joseph again.
"We've gone the distance in our last two fights.
"The plus side is he can do the 12 rounds, he can win the later rounds, his conditioning is good," said Barry.
"People are excited with knockouts. Joe hits hard and he hits fast and he's a very big, strong guy and I want to see all those things come into play in this fight."
After meeting Fury and his cousin, Tyson, in Manchester on media duties recently, and before that heavyweight rival and friend David Haye in London, Parker has just entered the second week of his camp in Las Vegas and, according to Barry, is working as hard as he ever has.
The contrast between the training methods of Parker and Fury is stark.
Parker, who yesterday was invited to attend a Floyd Mayweather training session in Las Vegas, is working day and night in Sin City in order to force the pace from the first bell.
Fury has taken a back-to-basics approach in England's tranquil Lake District.
"We've probably had one of the best first weeks we've ever had," Barry said.
"I think after doing that reconnaissance up in London and getting face to face with Hughie and having a look at the magnitude of this over there, I think Joe is heavily motivated at the moment.
"For me, that's a blessing. He always trains well. His last two fights, especially the most recent one, he was a little bit disappointed with himself. There were a lot of things going on but he knows he's capable of much more.
"Some of the things that we were doing to counteract the awkwardness and mobility of Fury, we're still doing that, but I've added a couple of things that I believe will make Joe more dynamic. And it's very important for him to be powerful and explosive in this fight. I want to get off to a really good start, not a lacklustre start. I don't want Fury to get comfortable at all."
Parker and Barry aim to be in the UK a fortnight before the fight. They will train at Haye's London gym before travelling to Manchester.
