I wouldn't be surprised if the club does some ticketed, commercial event at the Arena (or even at Anfield) and invites Klopp et al along for that.
The trophy parade should be for the current team and staff only, and I doubt that the guys who've left would disagree. Maybe if they put a stage up outside St George's Hall at the end they could invite them there, but not on the bus.
But I still recall that, during covid, Jurgen promised us a big, fuck-off party, and it never happened.