The Reds were linked with the 24-year-old during the summer transfer window, but the deadline passed with the Englishman still at the London Stadium.
Bowen has again been an important player for the Hammers this season, making seven appearances in all competitions, including five in the Premier League.
According to the Liverpool Echo, Liverpool remain admirers of the former Hull City youngster and could reignite their interest at the start of 2022.
The report claims that Bowen's 'tireless work ethic' makes him an attractive option for the Merseyside giants, who are keen to bring another attacker to the club next year.
Bowen, who still has four years left to run on his contract with the Hammers, has scored nine times and registered 11 assists in 60 appearances for David Moyes's side in all competitions. body check tags ::