There had been suggestions that the Uruguay international could be on his way back to South America, with the Brazilian side reported to be ready to offer £7million for his services.
Coates has struggled to make any real impact at Anfield since his arrival from Nacional back in August 2011, starting just five Premier League games in that time.
He had an opportunity to impress during Sunday's FA Cup fourth round clash with Oldham at Boundary Park, but endured a miserable afternoon as the Reds were beaten 3-2 by the League One outfit.
That had led to suggestions that Brendan Rodgers could be ready to part company with the centre-back and use any funds generated to bolster his squad.
But Gremio director Rui Costa has flatly denied that they are looking to sign the 22-year-old from the Premier League club.
Costa told UOL: "You can forget that, just forget it."