Liverpool were reported to have sent a scout to South America to watch Luan in action in Wednesday's 2-1 Copa Libertadores victory over Godoy Cruz, while Arsenal are also thought to be interested.
However, vice-president Odorico Roman insists the club have received no communication from the Reds regarding a potential swoop.
"I do not know of any other proposal," he said. "We had two firm approaches, from Sampdoria and Spartak.
"They were made, but Luan remains as a Gremio player at the moment."
Discussing his future on Wednesday, Luan said: "I will decide soon. My thoughts are still on Gremio.
"I saw people on social media asking me to stay. I know of the proposal [from Spartak] but we have to decide.
"On Thursday, I'll speak more calmly and give you the answer."
Luan made his senior Brazil debut in a 1-0 friendly victory over Colombia in January - the match played to benefit those affected by the Chapecoense tragedy - having played a key role in the country's Olympic success last year.