Jones, a central midfielder, had missed the previous two games against Aston Villa and Leeds United with a muscle injury.
Meanwhile, Nathaniel Phillips, Jordan Henderson, Joel Matip, Joe Gomez, Virgil van Dijk and Divock Origi remain on the sidelines.
Klopp revealed: "No, Nat Phillips is not back. Curtis is back, yes that’s true but all the others are not."
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The German also rubbished social media speculation suggesting Diogo Jota was set to miss the clash at Anfield: “Jota is fine.”
On the threat the Magpies pose, Klopp said: “Yes, they had a good spell at the beginning of the season and they dropped a little bit – they had injuries, Covid – everything came at once.
"Now I think they have a settled line-up even when they’re missing key players still with (Jamaal) Lascelles, (Fabian) Schar and others but now they play five at the back and Steve (Bruce) likes to keep the structure when it’s successful.
“Five at the back works well. (Jonjo) Shelvey, (Sean) Longstaff, (Miguel) Almiron – there could be some others as well in midfield.
"Mr (Allan) Saint-Maximin, he was injured and that was a massive blow for Newcastle and Joelinton, they play really well together.
"Wilson is then not even on the pitch – if he starts, that’s not a big drop performance-wise.
"They have found their line-up, their form and a way to play. For them, it’s good. For us, it’s a job to do.”