I voted NO - changing manager won't change outcome much under FSG, because problem isn't Klopp.
Bring the best tactical genius - he won't be able to do much if he doesn't get a squad for 38 match marathon. For any Manager, his problem will remain same under FSG. In fact, the higher the profile, hell have to go through the worst situation of his managerial career - wont get his first targets, have to wait till last week of transfer window to bring some spill overs because he'll have to sell before buying, have to buy what accountant tells him rather than whats needed, operate under strict wage cap and sell his best players for profit. On top of that, he has to lease his lip, tongue and a$$ to manage fans - its a dirty job Klopp has been doing to be honest.
We are scoring against Maribor and Huddersfield for fun, and in between failed to score against MU at home and got back side whipped at Wembly & Ittehad. This is a perfect example of what we call in cricket - glorified minnow basher - above average premadonas, who won't start for any of the top 5 teams, neither will be approached, unless on free transfer - it's Klopp that punching above weight with this bunch, but he has stressed his limit too much, something I stopped writing after 1st September closure of transfer window. My logic is simple - the team that Klopp assembling these days, for the greatest institution of British club sports (& 10th richest in football world), if this is the squad built by a Manager in his 3rd season and 5th window in a Champion's League year, that too after apparently owners made funds available - almost a quarter billion of it; you have to SACK the Manager by now ........ FSG has increased his wage for a 6 years contract extension. That's enough for those who can see the plot from synopsis.
If you ask me, the best manager for us and I am certain on this - Big Sam Alerdyce. Hell manage his Liverpool team for a confident mid table spot, hell manage his transfer budget & wage expenses the way Edwards tells him, may be with a bit of transfer profit as well, added sugar is an European trip once in every 2/3 years ..... and the day FSG appoints Big Sam, my expectation from Liverpool will also go to a proportionate level, which Big Sam can handle perfectly with his hoof ball and without out lip service.