The Brazil international had to be substituted during the opening fixture of the Premier League season against Norwich City, which Jurgen Klopp's men won 4-1.
Adrian has since deputised for the Reds, who have a 100 per cent record and are top of the table, two points clear of champions Manchester City, after four rounds of games.
The international break has given Alisson time to work on his fitness but John Achterberg indicated a return to action may not be imminent.
"In the last few days he has been out on the pitch to do some catching and footwork, as well as small passing drills," he told the Mirror.
"He has made steady progress. It needs time and we cannot look too far ahead, so we take each day as it comes, see how he feels, and then make progress from that.
"Ali has been working with Dave [Rydings, rehabilitation fitness coach] in the gym a lot to improve the strength and try to keep the fitness levels up."
Liverpool are at home to Newcastle United on Saturday.