The duo were part of the Uruguay side that bowed out of the Olympics in the group stages, but they have now joined up with new boss Brendan Rodgers.
Rodgers told reporters: "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.
"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."
Liverpool face FC Gomel in the second leg of their Europa League qualifier on Thursday.