The southern Italians head for the Camp Nou on Saturday with a first ever Champions League quarter-final berth beckoning.
“We certainly want to write an important page in our history,” said Gattuso of a feat which not even Argentine legend Diego Maradona managed to achieve with the club.
Both sides are 1-1 after the last 16, first leg in the San Paulo Stadium in February.
But Lionel Messi’s Spaniards have not been beaten at home in the Champions League in seven years as they target a 13th consecutive quarter-final berth.
Barcelona finished second in La Liga while Napoli were seventh in Serie A, but having secured a Europa League spot thanks to their Italian Cup victory.
Gattuso admitted his “head was already on Barcelona” as his side wrapped up their league season with a 3-1 win over Lazio last weekend.
“We will play on a high level stage and we want to be worthy of it,” he said.
“We know that if we want to compete against Barcelona we will have to take risks.”
The big question will be how to stop six-time Ballon d’Or winner Messi, a problem which former AC Milan midfielder Gattuso would have happily tackled as a player.
“I can mark Messi only in my dreams, or on my son’s PlayStation,” said the 42-year-old former Glasgow Rangers player, who won two Champions League titles with AC Milan.
“We are ready to face Barcelona. We have our style, we are prepared. But they have one player named Messi who can leave ten players behind.”
As a player, Gattuso had a fiery reputation, with a dogged never-say-die attitude.
– ‘God of football’ –
In Naples, more than rage he has brought calm to a locker room traumatised after a disastrous first half of the season under Carlo Ancelotti, his former coach in Milan.
This despite sparse coaching credentials, coming through Sion, Palermo, OFI Crete, Pisa and his beloved Milan before arriving in Naples.
He was harshly judged after his 18 months at AC Milan despite their fifth-place finish last season, missing out on the Champions League by one point.
But his successor Marco Giampaolo was sacked after just seven matches.
“It’s a profession that cannot be learned from books but by getting knocked in the teeth. I have had a few failures and will have many more,” said Gattuso.
Since the end of January, and after a difficult start to life in Naples with the team plunging to 13th position and Gattuso facing ridicule, the team have been reborn.
He has given confidence back to players including Lorenzo Insigne, Nikola Maksimovic and Kalidou Koulibaly.
His reputation as a 2006 World Cup star and two-time Champions League and Serie A winner holds weight in the locker room, along with his straight talking style, and work ethic.
“(Gattuso) Rino is the most respected coach in the dressing room since I have been here,” said Napoli owner Aurelio De Laurentiis.
Gattuso’s first trophy came in the Italian Cup just days after the death of his younger sister.
Napoli won a dramatic penalty shootout against Juventus in Rome for their first trophy in six years — a feat not achieved under Gattuso’s predecessors Maurizio Sarri and Ancelotti.
“There’s a God of football, who makes you reap all that you’ve sown,” said Gattuso.
“For me it’s serious work, which I do with great passion, I know I can’t relax for a second.”
In Barcelona, Napoli could be without forward Insigne, who has scored 12 goals in all competitions this season, as the Italy forward struggles with a thigh injury.
But club record scorer Dries Mertens, with 16 goals including in the first leg, will play along with Spanish midfielder Fabian Ruiz, hoping to make an impact on home soil.
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