Bilic added that Argentine midfielder Manuel Lanzini was set to make his comeback from a thigh injury against Southampton on Dec. 28.
"It is good news that Dimitri Payet is ahead of schedule. He should train with us after Villa and is with the fitness coaches now," Bilic told reporters on Thursday ahead of a weekend clash against bottom side Aston Villa.
"He might be involved in the Liverpool game, which would be a big boost for us.
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"Manuel Lanzini is progressing and will probably be available for the Southampton game. It looks like it will be the same squad as against Swansea for Villa, but we should have one or two back for Southampton."
Despite facing a Villa side on a 16-game winless run in the league, Bilic said he was not expecting an easy encounter.
"Every game is difficult in the Premier League and Aston Villa are struggling but they played a good game against Newcastle (1-1) last week," Bilic said.
"They are fighting for their lives and will have confidence from that away point. They have some quality players who can hurt you."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
