The Reds were first linked with the 24-year-old in 2016 and rumours have resurfaced in recent weeks following the departure of Philippe Coutinho to Barcelona.
According to a Yahoo! Sport report published on Wednesday, Liverpool were in advanced talks with Gremio and keen on meeting Luan's €18m (£15.7m) release clause ahead of next season.
A follow-up report in the Liverpool Echo poured cold water on the rumour and the player now has confirmed that, as things stand, the Merseysiders have not made as approach for his services.
"If I knew, I wouldn't hide. I always said that I would leave it to Gremio and to my agent, and if they had something concrete, they should talk to me," Luan is quoted by The Mirror as saying.
"No one has come to me, so there is nothing. It has to be good for me, it has to be good for Gremio. I will not rush to want to leave soon, just like in the middle of last year.
"For the moment that we were through, I decided to stay. It was my decision alone. Now it's the start of the season and I want to regain my form and rhythm to play. What I know is that I want to play the next game as soon as possible here at Gremio."
Luan has netted 18 times in 51 appearances for the Brazilian club.