Liverpool coach John Achterberg says he can't put a time frame on when Alisson will return to action due to the nature of his injury.
But Achterberg is hopeful that the Reds shot-stopper will be back between the sticks after the September international break.
Alisson tore his calf on the opening day of the season, as Liverpool battered newly-promoted Norwich 4-1 at Anfield.
Former West Ham goalkeeper Adrian, who was signed on a free in the summer, has been drafted in as his temporary replacement, but has since had his own injury problems.
Jurgen Klopp is keen to have his £67million number one keeper back in goal as his side look to get their Premier League campaign off to the best possible start.
But he may have to wait a little longer for the Brazilian to return.
"Ali is good," Achterberg told The Athletic. "He's in every day for treatment and they try to improve things.
"He's able to do some fitness work in the gym without using his leg.
"It's difficult, but you have to try to look forward and be positive. You have to try to turn a negative into a positive.
"They haven't given us a specific time he'll be out as it's difficult to say how quickly it will heal. That's all with the medics.
"There's an international break coming up and we'll have to wait and see how long it takes after that."
