But as the Reds returned to the AXA Training Centre this week ahead of the visit of Aston Villa to Anfield, the 32-year-old was not involved.
The midfielder, who underwent hip surgery in May to correct a long-term issue in the hope he would recover for the start of this season, has suffered a “little setback.”
“Curtis is back in training fully, Thiago not,” Klopp told reporters on Friday.
“Thiago had a little setback. [He] started training with the team and had a little setback, so we had to slow down there a little bit.
“It’s not cool for him, not cool for us, but that’s how it is.
“Thiago will use the international break for that obviously, to be up to speed. That should hopefully be enough.”
It is a frustrating situation for all involved, with Thiago unable to be involved at a time when Liverpool’s midfield is seeing wholesale change.
For the Spaniard, it appears to be showing, with these setbacks unfortunately to be expected for a player who, already prone to injury, has required surgery on his hip in his 30s.
His contract is due to expire at the end of the season, and it is increasingly difficult to see Thiago playing a key role between now and then.