With the Gunners fearing that Bukayo Saka could be out for up to eight weeks with a quad injury, the teenager could have an important role to play in the upcoming matches.
Dowman is likely to start in the Carabao Cup against Fleetwood on Tuesday night but the 16-year-old is also pushing for more Premier League involvement.
Arsenal host Everton on Saturday, the side Dowman came off the bench to deliver a sensational solo goal against last season and become the youngest scorer in Premier League history.
The England youth international has played only nine minutes in the league this season. However, Arteta is confident that the teenager will respond to the challenge when he is called upon for regular first-team action.
Opportunity: Max Dowman
Getty
Asked if Dowman has the potential to consistently deliver at first-team level, the Gunners boss replied: “He does.
"He needs more minutes to do that. It’s a lot to ask him to provide when he does not have a lot of minutes. It’s very difficult, probably unfair.
“But the moment that he starts to have more minutes and games I think he’s going to be able to do that because historically that’s what he’s done.
“The next step is obviously to another dimension and he’s more than capable of doing that.”
In his only senior start this season, Dowman scored twice in the Carabao Cup win over Ipswich.
He also netted for the England Under-19 side over the international break, though he was also then sent off against the United States.
Young star: Max Dowman
PA
Arteta admitted Dowman would be justified in thinking he has deserved more first-team opportunities, but the Spaniard is keen to carefully manage the trajectory that he is on.
"He needs to understand where he is at and where we are going to take him," Arteta said.
"And that is clear. It will not be a straight line up. Hopefully yes, but normally it is not like this.
"He needs to prepare for that but to have the spikes up and when the spikes are down, you better be ready because you never know the moment you are needed and there is no time to say, ‘no but I lack this’.
"That goes for every player but he is in a good place, he is training really well. When he had to play with us or the Under-21s he was the same and the same with the national team.
"We know the player we have and we need to give him the right chances and the right moments."
Arteta added: "He's a huge player for us, for our future, and probably he deserves more, so I accept that."