Jurgen Klopp hopes to have Joe Gomez available within four to six weeks, while Liverpool are set to be boosted by the return of three other injury absentees.
Despite initially being expected to miss only six weeks, the 21-year-old has not featured since that 3-1 win at Turf Moor, though an encouraging timeline for his return has now been set.
Trent Alexander-Arnold (knee), Jordan Henderson (muscle) and Georginio Wijnaldum (knee) - none of whom featured in the 1-1 draw at West Ham on Monday - are all closer to selection after completing training on Thursday.
Klopp did not confirm whether any of the trio would be involved against Bournemouth on Saturday but deemed defender Gomez's operation a success as the Reds seek reinforcements to correct the wobble that has allowed Manchester City to move back top of the Premier League.
"Joe's surgery worked pretty well," Klopp said.
"Recovery [timeframe] is always difficult but it's four to six weeks in terms of returning to play, so hopefully that's the case. We will work on that.
"Trent trained yesterday for the first time and didn't mention any problems. After three and a half weeks, four weeks, for a first session, we need to see what we do with that.
"Henderson trained yesterday as well for the first time. It was not that long a break but it's a muscle injury so we need to have another look today.
"Gini trained yesterday completely normal, but I don't know in this moment [if he can play against Bournemouth]. We have to see."
The hard work continues. pic.twitter.com/lQeN63zVyK— Liverpool FC (@LFC) February 8, 2019
Alex Oxlade-Chamberlain, sidelined by a knee injury since April, could be available for the quarter-finals of that competition should Liverpool advance past the Bundesliga champions.
"If we got to the semis of the Champions League again he should be available, quarter-finals maybe," Klopp said.
"We put him in the Champions League squad as we think there's the chance for him to play."