The 25-year-old has enjoyed an excellent time with the Hammers since making the £19m move from Hull City in January 2020, but particularly shone during the 2021-22 campaign for David Moyes' side.
Throughout 50 games in all competitions for West Ham, Bowen managed to find the back of the net on 18 occasions, whilst assisting 11 goals as well.
Such form has supposedly prompted interest from Arsenal this summer, according to The Beautiful Game Podcast, who report that the Gunners have begun negotiations over a potential move to the Emirates Stadium during the summer transfer window.
Leeds United's winger Raphinha is also said to be on the list of targets for Mikel Arteta's side, but it is Bowen that has become the priority as things stand.
Tweeting from their official Twitter account on Saturday, the podcast said: "Arsenal have opened contact with the representatives of Jarrod Bowen over a possible transfer. He's amongst their list of potential transfer targets, which includes Leeds United's Raphinha."
Bowen made his debut for England in the 1-0 defeat to Hungary last week, before coming off the bench in his country's successive draws against Germany and Italy in the Nations League.