The German international has been troubled by a back injury and has not featured for club or country since March, but had hoped to resume full training this week.
Monday was seen as an important day for Can's recovery, but scan results on his injury remain inconclusive and he has already been ruled out of Sunday's final Premier League game of the season against Brighton.
There is still a chance that the 24-year-old will be fit enough to begin light training at Melwood next week, which would give him almost two weeks to prove himself to manager Jurgen Klopp before the final against Real Madrid in Kiev on May 26.
But fears are growing that Can has played his last game for the club, with a free transfer to Juventus likely to happen this summer when his contract at Anfield expires.
Oxlade-Chamberlain will be missing until next season, but Lallana could play a part against Brighton after returning to training following a hamstring problem.
Liverpool are already without defenders Joe Gomez and Joel Matip for the rest of the campaign and must win on Sunday to ensure Champions League qualification for next season. Anything else could leave the door open for fifth-placed Chelsea to steal the final spot.