The 23-year-old has been sidelined since picking up an ankle injury against Brentford back in February and has missed the last nine matches in all competitions.
The Reds clinched a 2-1 victory over Brighton & Hove Albion on Sunday, with only Ibrahima Konate returning to the squad from those who were injured prior to the international break.
However, in his post-match press conference following the victory, Klopp confirmed that Jones is the next player set to return and could be back as early as this week.
«In full training is Curtis,» Klopp told reporters. «So he trained with us on Saturday but then had an extra [session] because the minus-one session (day before the game) is not the intensity that Curtis needed.
»So he was with us and then had an extra shift. So he will be in full training but then exactly for the game let me have a look on that. All the others, slowly but surely but not yet [for Thursday]."
Liverpool have been without a number of key players due to injury in recent weeks, but they were able to welcome Mohamed Salah back to the first team at the start of the month following the hamstring injury he sustained while representing Egypt at the Africa Cup of Nations at the start of the year.
The Reds' top scorer has started the last three matches in all competitions and has found the net in each, including the winner scored against the Seagulls over the weekend.
Andrew Robertson was left out of the squad that beat Brighton, though his return is believed to be imminent after scans showed no serious damage to the ankle he injured
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