The 29-year-old has not played since Liverpool's 4-0 defeat by Manchester United in Thailand earlier this month but is back in training at their camp in Austria.
Portuguese forward Diogo Jota (25) has already been ruled out of Liverpool's Community Shield clash with Premier League champions Manchester City on July 30 due to a muscle injury, but Klopp was more optimistic about Alisson.
"Obviously Diogo is not here, that's clear. But from the boys who are injured but are here, Ali is the closest - definitely not for Salzburg, but we will see. He is close to get back I think," Klopp said.
Klopp said several members of his squad had niggles.
"This afternoon is an important session as well. In this moment I don't know who can take part in it," the German added.
"We need to have a look and we'll play the game. It's pre-season so we have to get through it and then we have to deal with it."
Liverpool get their Premier League campaign up and running against Fulham at Craven Cottage on August 6.
