Jurgen Klopp has said it is unlikely Joe Gomez or Virgil van Dijk will be in action for Liverpool on Friday.
The pair returned to training this month following long spells out of action with knee injuries.
They were on tailored programmes separate from the main squad, but were handed more serious workloads on Monday.
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It was speculated that they could figure against Mainz in a pre-season friendly on Friday, but Klopp does not feel that will happen.
“It would be a surprise, to me as well,” Reds boss Klopp said when asked about the prospect of the pair playing on Friday. “They have looked really good in training and yesterday was the first day where they did very complex things, usually it is either offensive or defensive and stuff like this.
“We have to get there, step-by-step, but I don’t expect them for Friday.”
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Liverpool played two hour-long matches, back to back, against Wacker Innsbruck and Stuttgart on Tuesday.
Both games ended 1-1, and Klopp was happy with what he saw.
“It was a workout and it was good,” Klopp told the club’s official website. “Physically it was all that we wanted to see, we had to do it and it was an important test for that. From a football point of view, obviously a lot of space for improvement.
"I saw a lot of wild pressing. We wanted a wild press, we had a little competition between the two teams to see who wins the ball back more and how many counter-presses we have."
Konate made his debut for the Reds against Stuttgart, and Klopp was happy with the former RB Leipzig man’s performance.
“Ibou did really well and that’s what we expected; he looks really good in training,” Klopp said.
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