The 29-year-old defender suffered the injury against Wolves last month but Reds boss Jurgen Klopp remains hopeful he will be fit for the first leg of their Champions League last-16 tie against Bayern Munich on February 19.
“Dejan is not here and Joe (Gomez) is not here,” said Klopp.
“That’s never a good sign, I would say, but we will try everything to make Dejan available for Munich. It will be a tight race.
“For him, it makes sense in the moment to be in another place to do what he has to do.
“It wouldn’t have helped if he was here, so we will try everything – that’s clear.”
Meanwhile, James Milner, Georginio Wijnaldum and Fabinho did not train alongside their Liverpool team-mates in Marbella on Tuesday.
Milner and Wijnaldum had a separate session at the team hotel as they continue to build up their fitness following illness, while Fabinho has a ‘minor muscle complaint but is expected to resume full training in the coming days’.
“It’s how it is after games, you have a couple of problems,” said Klopp.
“Millie and Gini still struggle with their illnesses, so they did a bit of work in the hotel.
“Fabinho felt [something] a little bit; it will not be a problem, but there was no reason for him to be out today.
“Hopefully he can train tomorrow [Wednesday] and if not then the day after that.
“None of them are serious, all will be fine.”