When asked at a news conference whether he would be interested in signing Messi, Klopp replied: "Interest? Yeah, who doesn't want Messi in their team.
"But no chance. The numbers are absolutely not for us. But....good player. It would make it even more difficult to beat them [Manchester City].
"For the Premier League, it would be great. I would like to see it but I'm not sure if I will."
Liverpool face Arsenal in the Community Shield curtain-raiser on Saturday at Wembley (stream LIVE on ESPN+ at 11:30 a.m. ET in the U.S.) but Klopp does not expect his side to be on top form due to the short turnaround from the previous campaign.
"Would I want to play a proper game after two weeks prep? No," he added. "But we knew this for a while and we accept it. Two weeks training, worked hard and we saw that.
"We prepare for a whole season, an intense one. We don't have friendlies, we have testing games. It's a competition and it's rare you have perfect time to prepare for a game.
"We have four weeks which has been interrupted by internationals. I will be surprised if this is the best game we play but we are ready to fight."
The Liverpool boss also said there were no confirmed plans on how English football would respond to the developments in the United States.
A number of NBA, WNBA and Major League Soccer matches were postponed on Wednesday in protest of racial injustice and, in particular, the shooting of Jacob Blake, a Black man, by police.
"There's no real plans at the moment," he said. "It's about what the Premier League are saying and the boys.
"I've followed it in America, racism, Black Live Matter, all these things, dealing with it all will stay with us for a long time. As long as people don't really get or understand it, we have to mention equality."