From Joyce in The Times:
It is understood Buvac has become increasingly distant and withdrawn around the club, and visibly less engaged during matches recently, and it is that, rather than any specific fall-out with Klopp, which has resulted in his stepping back from first-team duties in the aftermath of the stalemate with Stoke City on Saturday. Liverpool’s players were informed at training on Sunday.
The decision appears to have been taken for the good of the club, with Klopp recognising that his assistant manager was not as engaged as in the past and opting to tackle the matter even at such a crucial time.
Klopp will hope his right-hand man can return, but if Buvac does not want to be around the club at present, when European ambitions are on the line, it is difficult to envisage that changing.
The coverage gets more exasperating as it goes on. The second paragraph above has since been removed from the online version. Is that because Joyce doubted his source(s), or perhaps realised that without further explanation it's just puzzling to state like that. If all that's happened is Buvac not pulling his weight, why remove him before the end of the season? For appearances sake, wouldn't it be easier to just leave him there? If he'd been active and giving dubious input, then yes, that might warrant removing him, but indolence surely wouldn't cause any serious problems for a few games. A withdrawn bloke on a chair is less eye-catching (and newsworthy) than an empty seat. I can't help but think that no hack really knows what's really going on.
Meanwhile, in the Mail, Dominic King (ex-Echo LFC corespondent, with contacts at least as good as Joyce's at the club) is reduced to speculating that it might be down to jealousy:
“One theory is Buvac has grown frustrated by a perceived dilution of his responsibilities, while Kornmayer, recruited from Bayern Munich two years ago, has been recommended to receive a new contract. Many have noticed of late that Buvac has seemed more distant”.
(I'm pretty sure it's not related to health or family, because when it is a club announces it's a personal matter and then they summon the core of local hacks, explain what the problem actually is, and then get them to agree to leave the story alone until a later date. That hasn't happened here.)