Luan, 24, has been heavily linked with a move to the Premier League this summer after turning down the chance to sign a new deal at the Brazilian club.
The Mirror claimed last month that Liverpool have been keeping tabs on the striker's situation over the last 12 months.
And it was suggested they were confident of sealing a £26million transfer after the player's advisor Jair Peixoto and agent Gianni Losito flew to the UK for talks.
However, according to Brazilian outlet Zero Hora, Luan is set to make a U-turn on his decision over a departure from Gremio.
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Liverpool target Luan looks set to stay at Gremio.
It is claimed he is now close to signing a contract extension with the Brazilian outfit.
Zero Hora say negotiations are at an advanced stage with the financial components of the deal already finalised.
This will come as a huge blow for Jurgen Klopp, who viewed the striker as the perfect man to fit into his fluid attacking system.
Klopp is keen to bolster his ranks ahead of next season as he embarks on a Premier League campaign with the added responsibility of Champions League football.
Liverpool target Luan looks set to remain at Gremio
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But a move for Luan now seems to be off the cards.
The Brazilian league is just two games into a new season and Luan has scored three goals in Gremio's opening three games.
He is currently contracted to the club until the summer of 2018.