Szoboszlai has been out since the 4-2 win over Newcastle on New Year’s Day, missing the last two games for Liverpool due to a hamstring problem.
There had been hope that the Hungary captain would return to fitness after a winter break that saw Klopp and his players take six days off.
A smaller-than-usual squad was put through their paces at the AXA Training Centre, with Szoboszlai one of 10 players currently out through injury or international duty.
Andy Robertson joined his team-mates in the gym as he nears a return following shoulder surgery, but there is no indication that he has resumed contact training.
There were also rare appearances for winger Trent Kone-Doherty, 17, and goalkeeper Kornel Misciur, 16.
Unlike Rhys Williams, who was recalled from a failed loan at Aberdeen this month before joining Port Vale on Tuesday, the club are yet to make a decision on whether Phillips and Beck will stay or go in January.
Calvin Ramsay, returned from a similar spell at Preston, is expected to head out on loan again and was not spotted in training.
Liverpool squad spotted in training on Wednesday
Defenders: Van Dijk, Konate, Quansah, Phillips, Gomez, Bradley, Beck, Scanlon
Midfielders: Jones, Mac Allister, Gravenberch, Elliott, McConnell, Clark
Forwards: Nunez, Jota, Diaz, Gakpo, Gordon, Koumas, Kone-Doherty