Gremio in talks over Ronaldinho return
"There exists an advanced contact between Gremio and the player's brother and agent," Gremio said on their website.
Club president Paulo Odone added: "I'm optimistic that we're going to sort the matter out on our part, pay up and bring him back to the club."
Ronaldinho was raised at the Porto Alegre outfit but left in acrimonious circumstances in 2001 to join Paris Saint-Germain.
The 30-year-old has fallen out of favour at Serie A leaders AC Milan, the latest unhappy episode in a career which began to go wrong following Brazil's quarter-final elimination at the 2006 World Cup.
The twice former World Player of the Year was left out of Brazil's World Cup squad this year but was recalled for last month's friendly against Argentina which Brazil lost 1-0.
Sao Paulo and Palmeiras are also reported to be interested in signing Ronaldinho, whose contract with Milan runs until the end of the season.