The controversial forward has joined up with the Reds squad alongside compatriot Sebastian Coates after Uruguay's Olympic participation came to an end.
Manager Brendan Rodgers is now close to having a full squad for the first time since his arrival, though Craig Bellamy has yet to join up with the Reds after Team GB's London 2012 exploits went on until Saturday.
Liverpool faces FC Gomel in the second leg of their Europa League qualifier on Thursday and currently holds a 1-0 aggregate advantage after victory in Belarus.
The recently appointed Northern Irishman expressed his excitement at working with the talented Uruguayan forward.
"It will be fantastic to have Luis coming back, and he is already fighting fit. He will have a couple of days off and join up with us after the weekend." Rodgers stated.
“He's been playing games, so he will already be up to a decent level of fitness, maybe even higher really, because he's had more competitive games. I'm really looking forward to working with him.”
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