I don't it see it happening and the news is FSG have left the decision to Klopp if he stays or goes.
Seems with this 6 year deal FSG have given him full control of all football matters,it was his decision to leave their training ground and build one next to the academy,all those issues Rodgers had with the transfer committee look to have gone as well.He has more control than he did at Dortmund where he had to work on player acquisitions with a general manager,he's there for the long haul it seems.
Coutinho will go after the world cup,the fee will be north of 100 million with PSG & (Neymar) and Barcelona wanting him and the RS will replace him with Keita who has a £50 million clause next summer.