Fa's stablemate Hemi Ahio (18-0), is also expected to fight on the same card.
Barry's latest heavyweight prospect Goodhall is scheduled to meet highly-touted countryman Justis Huni in Brisbane on June 15.
With Fa, Ahio and Goodhall all preparing for fights in June, they have reached an agreement to work together.
After striking a deal with Fa's manager, Mark Keddell, Barry and Goodhall will venture to New Zealand next month to spar with Fa and Ahio, giving the trio of heavyweights quality preparation for their respective, upcoming fights.
"It's good for Junior and Hemi because they are fighting on June 5 and it's good for us," Barry said.
"Mark and I have got a good rapport going at the moment so we'll take them up on the invitation and it'll be a win-win for both guys.
"Everything going to plan we're looking to go down to Auckland in the middle of May to spar with Junior and Hemi.
"I've seen Junior up close against Joe Parker. He's a very experienced, skilful guy. What I'm looking for with Justis Huni is someone with good head movement and the explosive style. Hemi is a little short but he brings all that so that will benefit us very much.
"City Kickboxing is on board. Doug Viney and Eugene Bareman said they'd love to have us in the gym. They've got an excellent facility there and I know they have other heavyweights. I thought it was a good opportunity. We were originally going to go to Brisbane two weeks out from the fight.
"Now we'll look at two weeks in New Zealand."
Barry notes the irony of preparing to work with Fa but explains he has adopted a similar open door sparring policy with his Vegas gym.
"Boxing is too small of a business not to welcome everyone in your gym. We have a lot of heavyweights in our gym sparring. I've had Goodhall working with the undefeated Tony Yoka, Joe Joyce, Jared Anderson, Christian Thun. That's through having the mindset of inviting people into the gym."
Goodhall and Huni were originally scheduled to meet in February, before the latter contracted Covid which forced the fight to be postponed.
Huni stopped Paul Gallen in the 10th and final round of their fight last June but Barry believes Commonwealth Games silver medallist Goodhall presents a step up in class.
"It's a great exciting fight for the fans. I started watching Justis Huni when he was 17 and I said to Dean Lonergan, before he set up his business in Australia, that this is the guy he should go after.
"I know a lot about him. He's only had five fights but he's very highly ranked.
"He was a very good amateur but so was Joe Goodhall – both guys were bronze medallists at the world championships.
"The two of them stack up very well. I believe, especially in the heavyweight division, you don't mature and develop into your body until your late 20s. Justis Huni is 23 – he's got plenty of filling out to do. Goodhall is 29, he's got his man body and strength. He's deceptively a very good fighter and he's shown me that in his sparring.
"He belongs in there and he's prepared very well."
