The 20-year-old has long been tipped for big things at the Gunners, but he has struggled for minutes this season.
Nelson has been restricted to just 81 minutes of action, which includes the Community Shield, and he was duly linked with a loan this summer.
The transfer window shut, however, with the forward still at Arsenal and Arteta has revealed that was partly because Nelson wanted to prove he can make the grade at the club this season.
“It was mixed reasons, Reiss was really convinced that he wanted to fight to stay here,” said Arteta.
“And when you see that willingness and that passion and that security in a player, you feel tempted to keep him even though you know that opportunities are going to be restricted and he is not going to have a lot of continuity in his play.
“We ended up with a large squad at the end of the transfer market. We had a few plans in mind with Reiss. One of them was as well to send him on loan to get more minutes because of the competition we have upfront.
“But things change very quickly and if he starts playing, and playing well, and he does what he can do, why not? He could start to play more games.”
Nelson will hope to be involved on Thursday night, when Arsenal take on Dundalk in the Europa League.
Arteta is expected to make changes to his side ahead of Sunday’s match at Manchester United, and Nelson is pushing to start after impressing in training.
“The reality is he has been really good in training. He wants to stay here. He wants to fight for his place,” said Arteta.
“That is what he is doing and he is going to get the chances in the right moments.
“What I am pleased with is how he has assimilated the situation – not playing a lot of minutes in the first few weeks.
“As everybody can see, things are changing very quickly. We are getting injuries. We will get more injuries because of the schedule that we have and he will get the opportunities.
“Then it will come down to him to take them or not.
“I try to have a very open communication with the players and try to get the doubts out of their mind, and try to talk clearly when they play or don’t play the reasons behind that.
“Most of the time they haven’t done anything wrong, it is just because there is a lot of competition for these positions and we are favouring other players in that moment. That’s it.”
While Nelson is available for Thursday’s match with Dundalk, Arteta confirmed David Luiz is out with a thigh injury.
Arteta added Luiz is “a big doubt” to play against Manchester United on Sunday, but Bukayo Saka and Willian are both training after injury scares.