Thiago sustained a calf injury during last week's home victory against Crystal Palace and fellow midfielder Keita hurt his foot in the midweek Carabao Cup win at Norwich.
On Thiago's injury, Klopp said: "It's not 100 per cent clear. It's a muscle in the calf. It's an issue, obviously. (He'll be back) after the international break probably. I don't think it would be anything earlier. We will have to see."
Keita was withdrawn at Carrow Road after catching his foot in the turf and Klopp added: "It's nothing really serious, but it keeps him out of the next game for sure, and maybe a little longer, we will have to see.
"It's nothing serious, but it's obviously painful and we have to see how we can deal with that."
Klopp made clear his admiration for the newly-promoted London club, who sit ninth in the table after winning two of their first five games, against Arsenal and Wolves.
"The football they play is incredible," Klopp said. "The organisation they have is incredible, so Thomas (Frank) is obviously doing a brilliant job. Brentford is doing a brilliant job.
"How they recruit, how different they are, how they show with less money that it's really possible to create something special.
"It reminds me a lot of my time at Mainz when I was there because we had no money and had to be creative in the transfer market.
"Brentford have a chance against us, not just because it's football, but because of the football they play.
"They're an incredibly well-drilled football team, a 3-5-2. Everybody knows what to do, everybody is ready to make the extra yard."
Liverpool, joint-top with Chelsea, have conceded only one goal in their first five Premier League matches and Klopp attributed that to his squad's collective defensive mindset.
Klopp added: "Ali (goalkeeper Alisson) in moments, he's made brilliant saves, it's not that nobody has had shots on target against us, but yes, as a unit so far we have defended pretty well.
"Nobody wanted to hear it, but we have three new players, without buying them – Joel (Matip), Joe (Gomez) and Virgil (van Dijk).
"Against Crystal Palace, the last line we changed completely, they never played together before, but it's not about that, you just need a clear defending attitude and that's what we have."