The midfielder reported to the Reds' pre-season training camp last week after an extended break following his participation in Euro 2020 with Spain.
While Thiago will sit out the team's pair of hour-long friendlies with the Serie A side, Klopp is optimistic he can make a full return to training next week.
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The boss told Liverpoolfc.com: "Thiago came here with a slight issue. He has three weeks off and the slight issue is still [there], which he was feeling.
"We don't take any risks. He's part of parts of training and in these little things he looks great, but it's more the longer distances where he struggles slightly.
"We have to make sure that will be sorted and we are on it. I think he will be in next week, [at the] latest, in full training."