The Schalke defender is out of contract at the end of this season, and was offered a new deal to stay in the Bundesliga.
However, after almost 16 years with Schalke, Matip turned down the contract offered to him, to move to the Premier League instead.
He was not short of admirers, and Liverpool managed to secure his signature on a free transfer, with Jurgen Klopp already moving to strengthen his team ahead of his first pre-season in charge at Anfield.
With Matip arriving on a free transfer, Liverpool are avoiding the need to pay a fee for him, but the BILD report indicates what they are paying in wages and a signing on fee for the Cameroonian international.
The Reds are paying roughly £5.5 million (€7m) in wages per year, as well as a signing on payment of £3.4 million (€5m).
Liverpool have got an excellent player for a budget fee in signing Matip on a free, but they will still be paying heavily for his services during his stay at Anfield.