Gattuso, a 2006 World Cup winner who played for Rangers in the late 1990s, was on Tuesday named by Italian media in a probe being carried out by Cremona's prosecuting office.
Ex-Lazio midfielder Cristian Brocchi is included in the investigation, according to reports.
Both face allegations that they were involved in a betting ring that fixed Serie A and other Italian games in the 2010-11 campaign.
Quoted in La Repubblica Sport, Gattuso told Sky Sport Italia: "Never have I ever had the slightest thought about possibly fixing a game.
"If something was proven I would be willing to go out into the street and, I know this is a strong thing to say, I would kill myself.
"Anyone who knows me knows that I can't stand to lose even a practice game, not even a game of cards with my friends.
"I'm angry and offended. I want to clear everything up so I don't have a stain on my career. I have never gambled in my life."
Reports in Italy claim that Gattuso and Brocchi both had telephone contact with people that were arrested on Monday night by police.
The four taken into custody are charged with sporting fraud as part of 'Last Bet' operation, an investigation that began in 2010 and that has already led to 54 arrests, including current and former Italian players.
"Gennaro is stunned by the news," Gattuso's agent Andrea D'Amico told Press Association Sport. "I spoke to him and he is returning home (to Milan).
"We are remaining calm and we have to be patient and see how the investigation develops.
"However, just because he is under investigation does not mean anything, for all we know this could be just false allegations.
"Sometimes when you are a famous player, it is very easy for your name to appear and to be a target.
"We will wait and see how the situation develops."
Gattuso, 35, retired from professional football earlier this year to pursue a coaching career.
He has been out of a job since being sacked as head coach by Serie B side Palermo in September.
Brocchi is currently a youth-team coach at AC Milan.