Speaking at a press conference on Tuesday, Cremona chief prosecutor Roberto Di Martino said Gattuso and Cristian Brocchi - another ex-Italy international - were connected to a case that saw four arrests made overnight.
Gattuso, who spent 13 years at Milan and won the World Cup with Italy in 2006, has vowed to clear his name, insisting he has done nothing wrong.
Gattuso, 35, told Sport Mediaset: "I'm angry and offended (by the allegations).
"I'm calm and I'm going to clarify everything.
"I do not want to have these marks on my career. I have never gambled in my life."
At Tuesday's press conference, Di Martino said: "Gattuso and Brocchi were connected to the case by the use of phone taps.
"The four people arrested are Salvatore Spadaro, Francesco Bazzani, Cosimo Rinci and Fabio Quadri, whom are suspected of helping connect fixers to players."
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
