Read an article earlier that Buvac was interviewing for 2 Managerial positions... 1 "definite" was the soon to be vacant Eintracht Frankfurt position because their Manager is taking over at Bayern next season and 2 is undisclosed but thought to be Arsenal.
Klopp and Buvac have apparently fallen out over Buvac's ambition to become a Manager elsewhere. They'd made a pact at Mainz years ago that whomever was a Manager the other would follow and become their Assistant. Buvac has played 2nd fiddle to Klopp for so long now that he wants to go it alone and test himself elsewhere.
I also believe this has been bubbling for sometime and that Stevie G naturally thought he would become Buvac's successor but was given the cold shoulder by Klopp. Stevie got p*ssed and sought a way out with Rangers learning of Stevie G's discontent!