The Brazilian midfielder will not be ready in time to face Southampton on Saturday but Brendan Rodgers could recall the Frenchman to the side after eight games out
Manager Brendan Rodgers confirmed on Thursday that the pair have rejoined the squad but only the Frenchman may be available for Saturday's trip to Southampton as his team-mate continues his rehabilitation from a knee problem.
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Lucas, meanwhile, will not feature on the south coast but is ahead of schedule in his recovery and Rodgers is prepared to be patient with both of them.
"We've obviously had a couple of players return to training," the Northern Irishman told the press. "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 in which 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."