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.