The former appeared a major doubt after being forced out of Sunday’s final Premier League game against Wolves at half-time with an Achilles injury, with the latter back from a hamstring complaint.
“Looks good for both Thiago and Fabinho,” Klopp said. “Fabinho trained completely normal.
“Thiago trained yesterday with the team, will train today and we will go from there.”
Meanwhile, Trent Alexander-Arnold admits it would be a privilege to win a second Champions League title at the age of 23.
The full-back is playing in his third final in five years, having lost against Saturday’s opponents Real Madrid in 2018, but winning the trophy against Tottenham 12 months later.
“To even be in with a chance of winning a second Champions League title at this young age is special, a privilege for me,” he said.
“I think you can try your best to say ‘it’s another big game’ but everything that comes around it, press conferences, media days, training on the pitch, is something we don’t do regularly.
“But we embrace the occasions, these are the occasions that are on your mind when you are working behind the scenes.
“I feel we deserve to be here. We haven’t got here through luck, we had an incredibly tough group stage.
“It’s the game of the season. To be here is good but to win it would be even better.”