The Brazil international had long been linked with a move to Anfield before the deal was confirmed on July 19, with neither Simon Mignolet nor Loris Karius convincing last term - the latter at fault for two goals in the 3-1 Champions League final defeat to Real Madrid.
And with the 25-year-old returning to training at the end of last week, Klopp says he is ready to pull on a Liverpool jersey for the first time in Dublin this weekend.
"It's pretty likely [he will play against Napoli]," Klopp told Liverpool's official website. "We should not waste time.
"Then it'll be nearly a week, or six days in training, since he [began training] and yes, he will play.
"I'm very pleased [to work with Alisson], but first of all it's very important he can start now because the season starts in one and a half weeks. Each player in the world needs training and time to adapt to his mates.
"We have two games to do that before we start, so it's really good. He obviously has a real presence, he's smart, he's very nice and it's good to have him around.
"It's only positive, even the performances in training – which is not too important in the beginning – are already exceptional, so all good."
Karius has been the Liverpool starter for most of the preseason, with Simon Mignolet on World Cup holiday and Danny Ward sold to Leicester City following Alisson's transfer.
After the match in Dublin, Liverpool will host a final friendly at Anfield against Torino on August 7 before getting their Premier League season underway at home against West Ham on August 12.