Coutinho was injured earlier this month against Swansea and needed an operation to stabilise the injury.
The Brazilian had started the season in superb form and Liverpool looked in need of his creativity at the weekend - after they lost 1-0 at home to Southampton.
But Coutinho has stated he is doing everything he can to be back playing as soon as possible - the initial assessment was that he would be back by the end of October.
"It's annoying to get injured, especially when you are playing well, but that happens," Globo Esporte quotes Coutinho as saying.
"I now want to focus on my recovery and do everything right to be back as soon as possible to help Liverpool in the league.
"The surgery was a success and this is what matters the most. I'll be back soon."
Coutinho is being strongly tipped to be part of Brazil's World Cup squad next year and he is hopeful of making the tournament in his homeland.
"I dream of getting called up again for the national team, but it's only up to me," he said.
"Of course it's bad when you get injured in a moment like this, but this is football.
"I have had a set-back and my concern is being fully ready as soon as possible. If I play well, things will happen naturally."