The report states that the Reds could make a move for the 25-year-old before the January transfer window closes.
However, the report further claims that it would take a bid of around £60 million to tempt the Hammers into selling Bowen this month.
Anfield Watch Verdict
We would not be against Liverpool making a move for Bowen at some stage. The winger is a good footballer.
Bowen has scored 15 goals and registered 20 assists in 82 appearances for West Ham United's first-team.
The Englishman has also been averaging a WhoScored player rating of 7.21 in the Premier League this season.
The aforementioned figures highlight that Bowen is capable of playing in England's top division of football.
With that being the case, the 25-year-old would certainly add depth and quality to Liverpool's forward line.