Police also arrested four individuals in connection with the case which is believed to have involved more than 30 matches stretching back to 2009.
"Rino was out and now he has come back home. We need to wait to understand more. His lawyers are in contact with the prosecutor," D'Amico said.
Gattuso, 35, twice won the Champions League with Milan. He was sacked as manager by Serie B Palermo in September after a string of bad results. Former Lazio, AC Milan and Inter Milan player Cristian Brocchi is also being investigated, officials said.
"It was a big surprise, we're all quite shocked. I've known Cristian for years and I think he's got nothing to do with any of this," Brocchi's agent Davide Lippi told SkyTG24 television. "Cristian is calm about it," he said.
Cremona chief prosecutor Roberto Di Martino told a news conference that investigators had identified telephone and SMS contacts between go-betweens and a number of players or individuals connected with teams ahead of matches.
The latest arrests and searches come after a three-year investigation which has produced evidence of an organised system among former and current footballers, sports betting operators and others to manipulate the result of dozens of matches.
Prosecutors say bets worth tens of thousands of euros, and in some cases hundreds of thousands, have been placed on both the top-flight Serie A and Serie B matches. The investigation was triggered by a second-tier Serie B match in Cremona in 2010 which aroused suspicions that led to a wider probe.
Former Lazio and Italy striker Giuseppe Signori was banned for five years and 15 other players have been suspended for between one and five years for their part in the scandal.
Di Martino said the case showed that the match-fixing scandal which has hung over Italian football since the 2006 "Calciopoli" scandal which saw Juventus stripped of the 2005 and 2006 Serie A titles had not been resolved.
"There hasn't been much reaction in Italy given that things have kept going as they were before," he said.