New Zealand could become Test rugby's leading nation for the first time in five years by beating Andy Farrell's men in Friday's blockbuster clash at a sold-out Aviva Stadium.
The Kiwis, who would also require world champions South Africa to lose to Scotland on Sunday for that scenario to materialise, are viewed as underdogs by bookmakers, despite defeating their hosts in the quarter-finals of last year's World Cup in France.
"Ireland have been right up there, not just the last few years, I think for the last 10 years they've been leading the way in a lot of areas," said Barrett.
"Us as All Blacks, we like to be in the picture in terms of the world No.1. That's a crown they've got at the moment.
"What more could you want than playing Ireland at home? It's going to be intense."
After dominating the fixture for more than a century, New Zealand have lost five of the last nine meetings between the countries, including a 2-1 series defeat on home soil in 2022.
Crusaders lock Barrett said that setback provided "easy fuel" 15 months later when the All Blacks gained revenge with a 28-24 last-eight win at the global tournament in Paris.
The 30-year-old expects Ireland to be determined to turn the tables this time around.
"It was one of the great matches at the World Cup," said Barrett.
"For us we know what Ireland are going to turn up with. That's a willingness to play and they'll be looking to put us under pressure.
"Last year's game, there were a lot of guys hurt by the series loss in 2022 back home, that was easy fuel and you are at a World Cup where everything is heightened.
"We love playing the big games, it's high pressure and what Test rugby is all about."
Former Ireland captain Johnny Sexton claimed he was taunted on the pitch by All Blacks centre Rieko Ioane following his side's World Cup exit.
Writing in his recently released autobiography, Sexton alleged Ioane said: "Don't miss your flight tomorrow. Enjoy your retirement, you c***."
"I guess there's a lot of feeling, it's Test match rugby and two teams that want to get a result so, at times, emotions can boil over and you've just got to be accurate with your game, and not after the whistle," replied Barrett when asked if there is bad blood between the rival sides.
But new Ireland captain Caelan Doris insists there is no ill-feeling between the teams.
"You obviously hear about some of the stuff that came out after the game (at the World Cup) but it hasn't been a big thing for us at all this week," the No.8 told reporters on Thursday.
"We're very aware of their threats and how good a team they are and how good the individuals are that they have, that's been the focus point more than anything else.
"Every time we play them, there is a good rivalry, mutual respect, these are two good sides going against each other."
with Reuters
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