Jurgen Klopp was eyeing a move for the Saints striker in January.
The Reds are thought to be in the market for a striker in January, with it having been a problem area for the side again this season.
Summer signing Christian Benteke has failed to impress, while Daniel Sturridge has once again failed to maintain his fitness for an extended period of time.
That had led manager Jurgen Klopp to identify Saints forward Long, but Southampton have rejected an approach for his services, with an £8 million move reportedly being eyed by the German according to the Mirror report.
Whether Liverpool will return with a firmer offer is as yet unknown, but it is thought that manager Ronald Koeman is determined to keep hold of Long regardless.
The Republic of Ireland striker is currently their joint top goalscorer alongside Graziano Pelle this season, with seven goals apiece in all competitions so far.
He will face further competition for a starting place in future though after the club completed a move for QPR striker Charlie Austin this week.