One of only four domestic-based players in Tite's latest national team squad, Luan starred at the 2016 Olympic Games and is on track to appear at next year's World Cup in Russia.
Liverpool continue to be linked with a move for Luan and Gremio boss Renato Gaucho admitted in June that it would be difficult to keep the player he describes as the best in Brazilian football.
However, Zanotta intends to open talks over a new contract when the 24-year-old returns from international duty.
"We do not intend to sell Luan. There are no more proposals," Zanotta told reporters after Gremio's 2-0 defeat to Cruzeiro.
"We have the chance to challenge for a title in two competitions [Campeonato Brasileiro and Copa Libertadores].
"We will let him come back from the Selecao and then take up contract talks very calmly."
The attacking midfielder's only other appearance came in a fundraising friendly for victims of the Chapecoense air disaster in January.