Alisson's Brazil team-mate Roberto Firmino also reported back for training after a break following the World Cup, and the pair could play a part in Liverpool's two remaining pre-season matches against Napoli on Saturday and Torino on Tuesday.
Liverpool's desperate need for a new goalkeeper was evident after Loris Karius' two bad mistakes in the Champions League final.
"I've also already worked with 'Mo Mo" (Salah), the three of them will be very important for me to settle into the squad.
After making five apperances for the Liverpool U23 team last season, Kelleher is looking to use his summer experiences as a springboard for a bigger role in the upcoming campaign.
"Then it'll be almost a week, or six days in training, since he (started) and yes, he will play".
And Klopp has made no effort to hide his delight at signing a player who is supposed to end Liverpool's long-standing goalkeeping woes.
"I wasn't expecting to play really, but to get the opportunity was just unbelievable", Kelleher said.
"This initial training session has been useful for me to see what our playing style should be in the Premier League".
"I trained with them [the senior side] last year but to actually play this year has been insane".
'It's important I get to know them as quickly as possible.
"The relationship we develop off the pitch is very helpful for us to gel as a team". They come in for the first time and I don't want to have that situation around the West Ham game, that they go kind of: 'Wow, that's Anfield!'
"My first impression tells me that it won't be hard for me here - it's a great squad formed by great players and brilliant professionals". However, the opposite occurred, as Liverpool didn't miss a beat without Coutinho, and the team finished runners-up in UEFA Champions League.
"Ojo played a fantastic pre-season, really good and confident technically, really strong, improved a lot in tactical things and his attitude was great", Klopp said.