Klopp refused to blame Mohamed Salah after the forward contracted Covid-19 having attended his brother's wedding in Egypt.
Salah, who is the joint leading scorer in the Premier League this season with eight goals, returned another positive test on Wednesday and is set to miss the Leicester game on Sunday.
"He is flying back today. I've been in close contact with him. When you have a negative test, the process starts. He has had no symptoms. Nothing to say in public about the situation," Klopp told reporters.
Klopp plays down prospect of Van Dijk or Gomez facing Mainz
"I was in Germany in the summer and a friend moved a birthday party for me and I decided not to go. It was allowed.
In other countries there's more social pressure and a brother's wedding is a special moment. My players are incredibly disciplined.
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Champions Liverpool are faced with a mounting injury crisis ahead of the clash against league leaders Leicester. Defenders Virgil van Dijk and Joe Gomez are set to miss the rest of the season after undergoing knee surgery.
Trent Alexander-Arnold, who was injured in the 1-1 Premier League draw with Manchester City earlier this month, and captain Jordan Henderson, who injured his leg on international duty with England, are also sidelined for Sunday's match.
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Tokyo 2020 (W)
Every Premier League player registered for the men's Olympic football event