The 16-year-old has strengthened his case for regular first-team involvement after scoring twice in the Carabao Cup win at Ipswich, while his England Under-19 performances have kept him in the spotlight.
Dowman scored against the Republic of Ireland before appearing as a substitute against Norway, although his international break ended with a straight red card against the United States.
The teenager will not be eligible for a loan move until he turns 17 on December 31. The January transfer window opens the following day, meaning Arsenal will then have the option to consider a temporary move.
The Standard reports that a number of clubs are interested in taking Dowman on loan, including West Ham. Arsenal, however, currently intend to keep him involved with the first team rather than actively seeking a destination for him.
That position is understandable given how closely the club have managed his development and the opportunities he has already been given by Mikel Arteta.
Dowman has trained alongside senior players including Bukayo Saka and Martin Odegaard, while he has also developed a close relationship with Declan Rice. Arteta has shown a willingness to trust him in competitive matches.
The manager has also made clear that a loan cannot be ruled out indefinitely.
“We will evaluate every six months where we are and what is the best thing for him to do and then make the right decision,” Arteta said.
“It depends on a lot of factors. What he needs, and what the team needs as well, the availability we have in the squad, the minutes that he is playing and the qualities of those minutes.
“We have to be open, but now the focus is to be here and to impact the team.”
Arteta knows from personal experience that young players can benefit from leaving their parent club. He joined Paris Saint-Germain on loan as a 17-year-old, but stressed that the environment and opportunities available to a player are crucial.
That is particularly relevant after Ethan Nwaneri's loan spell at Marseille failed to deliver the expected benefits. Arteta had wanted the midfielder to be “thrown in with the sharks”, but the experience underlined the importance of choosing the right destination.
For Dowman, Arsenal may not have that decision to make immediately. If his first-team opportunities continue to grow, the argument for keeping him at the Emirates could become stronger before January arrives.