The Mirror reports that Klopp agreed to the contract on Thursday and will fly into the northwest city in the evening to put pen to paper.
Klopp is rumoured to be bringing in long-time assistant Zeljko Buvac, and analyst Peter Krawietz, who were both with him during his successful reign at Borussia Dortmund.
The Guardian reported that Liverpool's two first team coaches Gary McAllister and Sean O'Driscoll were released from their positions earlier in the day. The two coaches were only hired in the summer.
The Liverpool board had hoped to have a replacement to ex-manager Brendan Rodgers announced by the weekend, and have slated a press conference to announce the appointment on Friday.
The club tried to lure the German to Anfield on two previous occasions, in 2010 and 2012, but both times Klopp turned them down.