The Brazilian side were reported to be closing in on a £7m deal to sign the Uruguay international, ending the defender’s miserable 18 months in the Premier League.
However, Gremio director of football Rui Costa has denied the club are interested in signing Coates, who featured in Liverpool 3-2 loss to Oldham Athletic in the FA Cup on Sunday.
“You can forget that, just forget it,” Costa told UOL.
Liverpool manager Brendan Rodgers criticised his young side for a disappointing performance at Oldham in the FA Cup fourth round.
Coates, 22, endured a difficult afternoon marking the physical Matt Smith, who scored twice as the League One side set up a fifth-round tie against Everton.
“We were coming here in good form and obviously we are bitterly disappointed,” Rodgers told BBC Sport.
“I was bitterly disappointed with the young players as today they had a chance to show they can play for Liverpool and compete for a club that has to challenge for trophies.
“We lost our concentration, and only had spells in the last 35 minutes when we were at the right level. Congratulations to Oldham, though.”
Coates has scored two goals in 22 appearances for the Reds after being signed from Nacional by former Liverpool manager Kenny Dalglish in 2011.