Even if true, the fact that the negotiations were carried out without Klopp's input doesn't mean it's without his blessing. He's made it known for a long time that he wanted the player.Also interesting note:
Someone who's normally spot on on another website (I won't link to it) has said that the VVD transfer was completely down to the boys over in Boston and no one in the UK (Klopp, Edwards, etc) had any involvement until they were told a few days later that it was all finalised. Basically, after the blunders over the summer, they took control and just paid up, no fuss.
Point being, it's also likely that Coutinho's transfer is also being sorted out by Boston directly meaning whether Klopp wants to force Coutinho to stay is irrelevant. If they're all about money and profit, he'll be off soon. If they recognise the football side of things, he'll be gone in summer.
I don't think you can read into that that they just go ahead and buy and sell without his agreement.