Speaking a day before Germany's Nations League game against the Netherlands, Klopp said the situation at FIFA was potentially worse than under Blatter, who stepped down amid a corruption scandal and later faced criminal charges.
"The opinion is unanimous that a change would make sense," Klopp told a press conference. "I didn't think things could get worse after Sepp Blatter, but someone managed to do just that."
Infantino, also Swiss, was elected FIFA president in 2016 after a corruption scandal brought Blatter's tenure to an end. Blatter was later acquitted in a Swiss criminal case concerning a two-million-Swiss-franc payment to former UEFA president Michel Platini.
"At the moment we think that if Infantino goes that then the next one could maybe do it better. I think it is possible to make it better," Klopp said.
"There are certainly people out there who care about the future of football and have no financial interest linked to that, and if they come together and one of them would become president, it would be helpful."
Infantino, who is up for re-election in March 2027 and who has vowed to stay on, came under heavy criticism in July after an unsuccessful attempt to bring private investors into a new FIFA commercial entity holding rights linked to competitions, including the World Cup.