But the England international, whose opportunities have been limited this season, will be sidelined with a hip strain despite now recovering from his virus.
Klopp told his pre-Arsenal press conference that Sturridge was "really, really ill" in recent weeks and now "has a strain in his hip muscle" which "happened in the rehab session.
He explained: "It's not the biggest one. It's very small, but it keeps him out of normal training for probably another week. In this week he can train, but not in team training."
The new injury problem comes days after Klopp told reporters he would wait until the end of the season to hold crunch talks with the forward about his long-term future.
Reds 'have to see' on Lovren
Klopp also issued an update on captain Jordan Henderson and defender Dejan Lovren, insisting that the club will assess the latter late on to decide if he can feature.
Klopp said that the visit of the Gunners "will be too soon, for sure" for Henderson, adding that the skipper's recovery "will take time."
But he continued: "Dejan, we will see. He [managed] part of team training the day before yesterday and then yesterday he was in full team training. Now we have to see how he reacts on this."
The German said that Lovren "will be involved in training again" provided that no-one from his medical staff says "anything different."
Dependent on his involvement in training, the club will "have to make a decision" on Lovren, Klopp said, insisting that his problem is "not the longest" but that he "was out for pretty much four weeks" and has only been back in training "for three days", adding: "I have to make a decision. I am not sure about it [at the moment]."
If Lovren is deemed fit enough to figure, it will be just the 13th time this season that he and Joël Matip - Klopp's first-choice centre-back pairing - have played together.