Kagawa was part of the Red Devils' most recent Premier League title-winning squad in 2012/13, which was also Sir Alex Ferguson's final season at the helm before his retirement.
Irvine is no stranger to competing at the highest level himself after appearing at three World Cups with Australia, but admits to being in awe of his current Cerezo Osaka teammate.
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"We’re not massively different in age, but I’m a Manchester United fan as well, and I've watched him play for years," the Australian explained to Flashscore during an interview in Japan.
"He's extraordinarily humble for what he's achieved in the game. He's vocal and helps the young players see the pictures he has in his mind.
"He's the kind of guy who wants to get your perspective on things and is a really open person. I love working with him, and he adds an incredible energy to the group.
"Knowing that you've got a player who's accomplished huge things in the game is a big boost to us as a team.
"He'll play a huge role for us, and I'm looking forward to seeing what we can do together this season."
Read the first part of our interview with Jackson Irvine here!
The 33-year-old also spoke in more detail about what convinced him to make the move from Bundesliga side St. Pauli over the summer, and revealed how a complete change of lifestyle was the ultimate factor.
"It's hard to kind of put it down to just one reason. I think you get to moments in your life and your career when you need a change," he added. "This definitely was one of those moments for me and my family.
"Japan as a country and a culture has always interested us. I’ve always been a big fan of Japanese football, with a lot of brilliant players emerging from this league, and a lot of Australian players coming to play here too.
"When the opportunity came up, I had a couple of conversations and had a very good feeling from the start.
"I am quite an instinctual kind of person, and I had a very similar feeling when I went to my last club, St. Pauli.
"Sometimes you just feel like this is the right place for me right now, and I definitely had that feeling coming here."
The J1 League as a whole is also gaining more prominence, and Irvine has been impressed by the division’s attacking quality in particular.
"It's hard to compare to the Bundesliga, as you're talking about one of the top two or three leagues in the world.
"But in terms of the individual quality in the front third in particular, I think this league is extremely strong. The one-against-one speed and the directness of the front players have really impressed me.
"It hasn't shocked me, considering some of the players that have come from Japan to play in Germany.
"Personally, I want to see how far we can push this team. We've got some amazing experience and some players in this division that know the league inside out.
"We've got some brilliant young players, and I think we've balanced that off with me coming in as well. It all adds to a healthy dynamic within the squad."