But the imminent boost to Klopp’s options is a welcome one with Liverpool engaged in a Premier League title race and still in the Europa League.
Alisson has been sidelined since February with a muscle complaint, while Alexander-Arnold and Jota were struck down that same month with knee issues.
Key names rejoin a strong squad
Mohamed Salah, Luis Diaz, Dominik Szoboszlai, Alexis Mac Allister, Cody Gakpo and Curtis Jones were among those also spotted in early footage.
They were joined by a youthful core, with Jayden Danns, Bobby Clark, James McConnell, Kaide Gordon, Trey Nyoni and Lewis Koumas all training.
Joe Gomez, Kostas Tsimikas and Jarell Quansah could all be seen, too.
Alisson has missed the last 13 games after injury ruled him out for over two months, with Caoimhin Kelleher filling in admirably since.
Alexander-Arnold has sat out of 12 games so far and Jota 11, though that tally could increase before they return to action.
Bajcetic, meanwhile, has featured only twice this season due to a persistent adductor issue.
When they are passed fit to feature again, that would leave only Joel Matip, Thiago and Ben Doak on the sidelines.
Liverpool squad pictured training on Tuesday
Goalkeepers: Alisson, Kelleher, Adrian, Mrozek
Defenders: Van Dijk, Konate, Quansah, Gomez, Alexander-Arnold, Bradley, Robertson, Tsimikas
Midfielders: Mac Allister, Szoboszlai, Endo*, Jones, Elliott, Gravenberch, Bajcetic, Clark, McConnell, Nyoni
Forwards: Salah, Nunez, Diaz, Jota, Gakpo, Danns, Koumas, Gordon