The implication of 'he only manages Dortmund and Liverpool' is that he would do better at a club with less restrictions which is practically proven false with Klopp turning down a club with less restrictions.
https://www.telegraph.co.uk/football/2017/10/12/jurgen-klopp-turned-chance-manage-man-utd/
Jurgen Klopp was asked to succeed SAF, he was going to inherit a title winning squad and get a truckload of money. A long time acquaintance of Klopp from Mainz said that
Klopp's dream team to manage in England would be Manchester United. The only logical explanation is that he chose Liverpool because that was his highest chance of success. This makes him managing teams with less money irrelevant because that is his path of least resistance.
I believe come the end of the season the reason for his reluctance to manager elite clubs will be confirmed (with Liverpool finishing 2nd).
Liverpool spent £150m in the summer and might not have a trophy to show for it, that signals the end of your tenure at a club like Madrid, Barca, United etc. Liverpool will probably be fine with Klopp because of their trophy drought. However, they aren't the plucky underdogs anymore with breaking world record fees for defenders and goalkeeper.