Curtis Jones and Joel Matip were pictured taking part in Monday afternoon’s session at the AXA Training Centre ahead of the Reds' meeting with Newcastle United in midweek.
Meanwhile, Jota, Thiago Alcantara, Caoimhin Kelleher and Calvin Ramsay are also continuing to make encouraging progress with their rehabilitation.
Speaking at a press conference on Tuesday, Klopp said: "I think Diogo can train from Thursday on and Thiago I think slightly later, so we will see.
"Calvin is getting closer, Caoimh I saw now only walking outside going for normal goalkeeper training. So yeah, there’s light at the end of the tunnel, definitely."