The 25-year-old scored his fourth and fifth Premier League goals of the season against the Canaries, as David Moyes's side strengthened their hopes of a top-four finish with a 2-0 win.
Bowen has been in impressive form for the Hammers this season, scoring eight times and registering 10 assists in 30 appearances in all competitions, and Jurgen Klopp's side are said to be admirers.
According to Football Insider, the Englishman was watched by Liverpool scouts on Wednesday, with the Reds continuing to monitor his performances this season.
The report also claims that Bowen is aware of the interest from Anfield and would be 'open' to moving to the Merseyside giants during this summer's transfer window.
The attacker, who has a contract at London Stadium until June 2025, has scored 17 goals and registered 20 assists in 83 appearances for West Ham in all competitions. body check tags ::