The pair have been sidelined since the start of January, with hamstring and calf problems respectively, with Milner missing four games and Shaqiri playing one of the last seven.
Southampton head to Anfield this weekend for the Reds’ last game before the winter break—with Klopp and his first-team squad not involved against Shrewsbury in midweek—but neither Milner or Shaqiri will be available.
“Divock was a cramp,” he said, after the Belgian’s late withdrawal at West Ham, “he should be in training today.”
Klopp therefore has plenty of options to consider for his squad at Anfield, though he is unlikely to make many changes with two weeks’ rest to come afterwards.
The most feasible change is for Minamino to replace Origi in the attacking line, though Curtis Jones could also be an option after his cameo role at the London Stadium in midweek.