Suarez returned to boyhood club Nacional in the summer, after his departure from Los Rojiblancos, and despite inspiring them to the Uruguayan title, his short term deal expired.
The terms of his previous agreement only tied him to the club until after his World Cup duty with Uruguay this month.
Gremio vice president Paulo Caleffi confirmed the club are in talks with Suarez’s representatives 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.”
According to reports from Marca, Suarez has already arrived in Brazil to undergo a medical, ahead of signing an 18-month deal in Porto Algere.
The report adds fans are so excited over Suarez’s impending arrival, that the No.9 shirt has already sold out in the club shop, with confirmation of the move expected in the coming days.