Liverpool manager Jurgen Klopp said centre back Virgil van Dijk had made good progress in training as the Dutch international prepares to return from a serious knee injury.
Van Dijk, 30, has been sidelined since undergoing surgery on the injury he picked up in the Premier League match against Everton in October.
Van Dijk, Joe Gomez (knee), Joel Matip (ankle) and Trent Alexander-Arnold (thigh) are all working on their fitness and took part in Liverpool's pre-season training in Salzburg, Austria.
Klopp told the Liverpool website: "Virg and Joe will not have double sessions now for the first few days with the team. I don't know exactly when we can make the next steps but it will happen in the next four weeks, for sure – we will get a big step forward.
"Joel looks good, absolutely, he is the closest probably to normal training... Trent was a serious enough injury but now not a major one, I would say. He is close but in the moment, probably the next five or six days he has a special programme."
Liverpool, who finished third last season, begin their new league campaign at promoted Norwich City on 14 August.