The German striker was linked with the Reds as a potential back-up to Mohamed Salah, Roberto Firmino and Sadio Mane, with Daniel Sturridge departing Anfield this summer.
The 31-year-old is out of contract and will be moving on a free transfer, however, the ECHO understands Kruse is not someone manager Jürgen Klopp is looking to add to his fold.
Kruse is an ageing frontman and the Reds would clearly rather put their faith in the young Brewster as a promising up-and-coming talent.
The club will also hope Origi puts pen to paper on a new contract and extends his stay with Liverpool, while continuing to make a huge impact in similar vein to the way he did last season.