The summer signing has endured a stuttering start to life on Merseyside, with a positive coronavirus test result quickly followed by an injury in the Merseyside derby.
Thiago was pictured working away from the group at Melwood as he works back towards a return to action.
Jurgen Klopp confirmed Joel Matip and Naby Keita will join Thiago Alcantara on the sidelines for the visit of Danish minnows FC Midtjylland.
The weekend visit of West Ham is a more likely return date for the former Bayern Munich midfielder.
Klopp has been counting the cost of Liverpool's injuries, most notably to talisman Virgil van Dijk. The manager believes his team are doing as well as can be expected without "the best defender in the world."
"Every team in the world would miss Virgil van Dijk," said Klopp at his pre-match press conference. "He is the best in the world. You play a game, he gets injured, and you play three days later so of course that's difficult to do because all the boys played together with him and we didn't have long for them to get used to playing without him.
"Fabinho, who normally plays as a six, has had to come in and play with Joe (Gomez). For that we did pretty well and that will get better 100 per cent because unfortunately everything in life takes time and defending takes time.
"They all played with Virgil at some point but not many times did they play together with each other so we do not expect perfection - but not too far away from perfection. Everyone needs time to replace a massive person or player, Virgil is the best defender in the world and so far we've done pretty well."