Thiago, 30, has impressed at the start of the campaign but limped off during Liverpool's 3-0 win over Crystal Palace last weekend.
"[He'll return] after the international break probably, I don't think it's possible he'll be back anytime earlier so we will have to see."
Thiago is set to miss crucial games against Porto in the Champions League before Liverpool host Manchester City next week. The club will be hopeful he can return for the trip to Watford on Oct. 16 after the international break.
The midfielder moved to Anfield from Bayern Munich last summer but his debut season was hampered after picking a knee injury in the Merseyside derby last October.
Klopp also said he was impressed with Brentford's debut campaign in the Premier League and praised the club for their recruitment policy.
"I watched the press conference of Thomas Frank and it was like one of the most entertaining things I watched for the last few years," Klopp added.
"It was really good. The football they play is incredible and the organisation is incredible so Thomas and Brentford is doing an incredible job. They show even with less money you can create something really special.
"They are incredibly well-drilled football team. Everyone knows what to do, everyone is ready to make the extra yard. I saw them celebrating after the Arsenal game which was absolutely great to see how much it meant to them and we know what we have to expect them."