The report claims Aogo, who is currently on loan at Schalke from Hamburg, is available for £2.5m at the end of the season. Schalke thought they had the first-option on the Germany international.
But German newspaper Bild reports that Aogo is free to negotiate a better package elsewhere if he wants, with Liverpool, Bayer Leverkusen and Roma all preparing offers of their own.
The left-back has represented Germany 11 times since his national team debut in 2010, and could offer competition for Jose Enrique.
Liverpool brought Aly Cissokho to the club on loan over the summer, but the wing-back may return to Valencia at the end of the season.
Should that happen, Brendan Rodgers would be back in the market for a left-back, and the report claims Aogo is a potential target.
Liverpool have the budget to offer him a competitive deal, but any move would not materialise until the end of the season at the earliest.
An attacking full-back, Aogo would fit Rodgers' recent preference for a three-at-the-back system that utilises quick, counter-attacking wing-backs.