Thiago underwent surgery to correct a long-standing hip injury towards the end of last season, and three months on he is yet to fully recover.
The 32-year-old has joined various sessions at the AXA Training Centre, but as it stands has not been a regular in first-team training.
But as a 30-man squad stepped up training on Wednesday, there was no sign of the Spaniard.
Other academy players involved were Luke Chambers, Lewis Koumas and goalkeepers Marcelo Pitaluga, Vitezslav Jaros and Fabian Mrozek.
Pitaluga, 20, received glowing praise from Van Dijk and Mohamed Salah for a series of saves during a shooting drill.
Thiago was at the AXA Training Centre on Wednesday, but is likely to have followed an individual programme having not joined his team-mates.
The ongoing recovery of Thiago will remain a concern for Liverpool staff, though caution will be taken with his reintegration either way.
Given the nature of his injury and the necessity of surgery, there could be genuine worries over Thiago‘s long-term fitness moving forward.
However, the hope is that, once fit, the veteran can produce a consistent final campaign at Anfield ahead of an expected free transfer next summer.
Celta Vigo will be among the clubs interested when his contract does expire, with Thiago‘s father, Mazinho, admitting this week that he would like to see his son return “home.”
Liverpool squad in training on Wednesday
Defenders: Van Dijk*, Gomez, Matip, Quansah, Alexander-Arnold, Robertson, Tsimikas, Chambers
Midfielders: Szoboszlai, Mac Allister, Endo, Jones, Elliott, Bajcetic, Morton, Clark, McConnell
Forwards: Salah, Diaz, Gakpo, Nunez, Jota, Doak, Koumas