The Brazilian stopper has attracted transfer interest from his native country with Flamengo one of the clubs eyeing up a possible offer.
However, there’s no universal agreement on what package can be put together back in Rio de Janeiro, despite the option to land the 34-year-old as a free agent.
Alisson's high wages are also an issue, and the former AS Roma star has now confirmed his plan is to renew, with extension talks ongoing.
"Yes, I want to stay. I'm focused on playing every game, but in my mind I'm happy to stay.
"It also depends on lots of aspects and different situations. But my will is to stay - I'm happy here and my family is happy too.
"I'm still hungry for titles and delivering good performances. I want to play at the top level for as long as I can."
Alisson has made over 350 club appearances since joining the Reds back in 2018 - and he's won two Premier League titles and a UEFA Champions League crown as their No.1.