Xherdan Shaqiri, another new signing who has hit the ground running, played the ball across goal for Grujic to tap in during the training drill, but Alisson was alive to the danger and sprung across his goal to deflect the ball over.
And, at least provisionally, Alisson will not be Liverpool's number one but their number 13.
Loris Karius now occupies the No. 1 squad number at Liverpool, while Simon Mignolet, who could leave Anfield this summer, wears No. 22.
Playing against Napoli will be a familiar experience for Alisson despite making the switch from AS Roma to Liverpool last month.
Liverpool released an official statement announcing Alisson's "provisional" number, and confirmed that the goalkeeper will be assigned an official number in due course.
The obvious example of this is Trent Alexander-Arnold, who was given the opportunity to cement his place in the German's starting XI last season at just 19 years of age.
Alisson started training with Liverpool earlier this week following a break after Brazil's World Cup campaign. "We should not waste time", Klopp told Liverpool's website.
"I hope I can help and bring something extra to the team". Each player in the world needs training and time to adapt to his mates. He will be looking to step up his preparations to be fit in time for the opening Premier League game of the season against West Ham United.
"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", Klopp continued.