The former Liverpool manager, now in charge of Germany, was asked about the possibility after Tuesday's verdict found City guilty of all the serious financial charges brought by the Premier League relating to the 2009-18 period.
City's dominance during that era regularly put them in direct competition with Liverpool, with Klopp overseeing several fiercely contested title races. Liverpool finished just one point behind City in both the 2018-19 and 2021-22 campaigns, with both seasons producing exceptionally high points totals.
Klopp did eventually guide Liverpool to the championship in 2019-20, his only Premier League title with the club.
Despite the latest developments in City's financial case, Klopp's admiration for Pep Guardiola has reportedly remained intact. Guardiola managed City from 2016 until his departure in 2026.
"I know I once said something that I'd come if there was ever a parade, but it doesn't feel like that now. I don't feel like I need to have my bus parade. I can wait and stay totally relaxed," Klopp told a news conference.
"My respect for Pep Guardiola and the football that City played in the time when we played against each other, what they played on the field, the opponents they were at the top level, is much too high for me to say anything now.
"If there are some punishments handed down, then it's obviously not anything to do with me so I'll just wait. I'm completely OK about what happened and what we achieved."
Manchester City are expected to lodge an appeal against the Premier League's findings that the club breached financial rules, opening the next stage of a case that has been running for several years.
Arsenal have been handed another injury concern after Christos Tzolis was forced off during Greece's 2-2 draw with the Netherlands in the UEFA Nations League on Thursday.
Jurgen Klopp has praised Germany's all-round performance after they claimed their first win under the former Liverpool manager with a 2-0 victory over Serbia at the Allianz Arena in the UEFA Nations League.
Tottenham chief executive Vinai Venkatesham has defended head coach Roberto De Zerbi despite the club's difficult opening to the Premier League season.
