Bowen - who joined the Hammers from Hull City in January last year - was said to be on the Reds' radar during the summer.
The 24-year-old has continued his strong showings for David Moyes' side early this season, starting six of their seven games in all competitions so far - and coming off the bench in last week's Europa League win away to Dinamo Zagreb, his European debut.
And the Liverpool Echo suggest that, should the versatile attacker - while at his best wide right, Bowen can operate across the front line - keep up his high performance levels, Liverpool could swoop for him when the next transfer window rolls around a few months from now.
It's not hard to see why Jurgen Klopp might be a fan. Bowen may only have scored nine goals in 56 Premier League appearances - having been prolific at Championship level - but he's a true grafter and would suit Klopp's gegenpress down to the ground.
And in a team who create as much as Liverpool - only Manchester City rank ahead of them in the expected goals stakes so far in 2021/22 (per Stats Perform) - the goals are bound to follow.
Besides, the Reds have good form when it comes to making shrewd acquisitions by targeting perhaps less obvious players.
Case in point: Andy Robertson - who signed directly from Hull and had only made 24 top-flight appearances - and Joe Gomez - who had only played in the Championship with Charlton. Both were integral to the Liverpool's 2019/20 title win - and it wouldn't be a surprise to see someone like Bowen follow in their footsteps.
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