Gremio president Romildo Bolzan Junior hopes to hold talks with Edinson Cavani over a move to the Brazilian club.
Cavani is a free agent, having left Paris Saint-Germain at the end of his contract in June after seven successful seasons in Paris.
The club's all-time record goal-scorer with 200 in all competitions, Cavani has been linked with a host of European clubs including Inter, Bayern Munich and, more recently, Barcelona.
It has also been suggested the 33-year-old could choose to return to South America, with Gremio among the clubs said to be interested.
Vice-president Paulo Luz denied holding talks with Cavani's representative, but Romildo does not appear ready to abandon the dream of signing the Uruguay star.
"He [Cavani's agent] didn't make a proposal. But in life, if you don't talk, you don't know anything," he told Hora do Consular.
"Suddenly, there is chemistry, something different, empathy, a desire, and then suddenly it happens.
"Rationally, if things were under normal conditions, we wouldn't have the slightest expectation of bringing in this player because he wants to play in Europe, he will have offers a thousand times greater than those that a South American and Brazilian team can offer.
"Now, if he has it in his head, his idea, his desire, to do a project that is close to his home, close to his businesses and close to Uruguay, I believe he could sit down with us.
"I have this expectation that he has this feeling, and that he can talk to us a little more."
Cavani won 19 trophies, including six Ligue 1 titles, after joining PSG from Napoli in 2013 for a reported fee of €64million.