Suarez returned to his boyhood club Nacional in the summer, following his departure from Los Rojiblancos, and despite inspiring them to the Uruguayan title, his short term deal expired.
The terms of his agreement only tied him to the club until after his World Cup duty with Uruguay this month.
Suarez has previously hinted at a desire to return to Europe, alongside interest from MLS, but the veteran striker is likely to prefer remaining in South America, over a move north.
Gremio vice president Paulo Caleffi confirmed the club will open talks with Suarez’s representatives in the coming days as they look to secure a deal.
“We’re going to have a conversation with Suarez’s representatives”, as per reports from Diario AS.
“Although it has been mentioned several times that we already met, a definitive conversation is yet to occur. This week is when the final meeting will take place.”
Suarez turns 36 in January, but he is determined to play on for at least another 12 months, before retiring.