"He is much better. It's still a bit painful, nothing else," Klopp told reporters ahead of the League Cup third round clash at Anfield.
"We will see how we deal with that. It's not too serious, but it's not nothing, so that needs to settle for sure. We will see how he is today and make a decision about him."
If Van Dijk is ruled out, the experienced Lovren could fill in. The 29-year-old has not played this season after aggravating an earlier pelvic injury during Croatia's march to the World Cup final in Russia in July.
"Dejan looks quite good. He trained completely normal now four times. He worked with the fitness guys before that for 10 days. He looks ready," Klopp added.
Klopp said first choice goalkeeper Alisson would be rested with Simon Mignolet taking his place. The German, however, said he would field a strong side against Maurizio Sarri's team.
"It's a competition we like... It's a difficult draw for both teams. It's not that you think the first two-three rounds you go through somehow, and from the semis on it starts getting exciting... It's a home game against a very strong side, so it'll be really interesting."
Liverpool return to Premier League action on Saturday, when they face Chelsea for the second time this week, away at Stamford Bridge.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Hugh Lawson)
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