Manager Brendan Rodgers confirmed on Thursday that the pair have rejoined the squad, but only Sakho may be available for Saturday's trip to Southampton as Lucas continues his rehabilitation from a knee problem.
France international Sakho has missed Liverpool's last eight Premier League games after sustaining a hamstring injury in the 2-1 defeat at Chelsea in December, and is set to undergo a late fitness test to determine if he can play at the weekend.
Lucas will not feature at St Mary's, but is ahead of schedule in his recovery and Rodgers is prepared to be patient with both him and Sakho as they return to the first-team fold.
"We've obviously had a couple of players return to training," the Northern Irishman said. "Young Sakho has trained this week, which has been great. We'll see if it's too early for him this weekend.
"And Lucas Leiva rejoined the group today, which was great."
Long-term absentee Jose Enrique continues to be sidelined, although Rodgers is pleased with the way the full-back is recuperating from his knee injury.
"Jose Enrique is still out," he added. "It has just been ongoing.
"He has obviously got the issue with his knee; he has come back after a good spell in America.
"He is rehabilitating well, there's no timeline on it. I trust the medical team here, they are very good and will advise me when he's nearly fit."
