Robertson has been sidelined since November after dislocating his shoulder while on international duty with Scotland, missing the last 20 games.
Alexander-Arnold and Szoboszlai, meanwhile, picked up knee and hamstring injuries, respectively, during Reds games earlier this month.
Asked about Alexander-Arnold, who spent the winter break at a Prada fashion show in Milan, the German joked: “He can walk… on the catwalk!
“They’re all positive but not ready,” he continued. “They’re all going in the right direction and getting closer and closer and closer, and some of them might be in team training next week.
“But for the Bournemouth game, I don’t expect anyone back.
“Trent close, Dom close, Robbo close. They are all going in the right direction but for this weekend’s game, no.”
That would then put them in line for a comeback when Chelsea visit Merseyside on January 31.