Arteta, who played for Arsenal between 2011 and 2016, was appointed Unai Emery's permanent successor at the Emirates Stadium in December.
He has won just one of his seven Premier League games in charge so far, and Arsenal remain mired in mid-table:
But the Gunners' performances have improved.
Before moving back to north London to take the top job, the Spaniard was working as one of Pep Guardiola's assistants at City.
Nelson, 20, believes Arteta played a major role in the improvement of players like Sterling and Sane at the Etihad Stadium, and he is confident his new manager can have a similar impact on his game, per Simon Collings of the Evening Standard:
"It is crazy because you look at Sterling and Sane and you see them before at their previous teams, they weren't doing what they do now. I think that is credit to Pep, of course, but Mikel as well because they said he did a lot of one-to-one work with them.
“You can see it because Mikel's drive is different. I haven't seen a manager with that much determination to make individuals into better players. I have all my belief in Mikel, and I think he is going to make me into a top player."
Before Emery was sacked, Nelson played only 151 minutes in the 2019-20 Premier League.
Under Arteta, he has already played 197 minutes in the English top flight, and he has not even been available for recent matches because of a hamstring problem.
It is clear that Arteta sees Nelson as a key part of his first-team squad.
An Arsenal statement at the end of January said Nelson was set to return to full training during the current winter break, so he could be available again for Sunday's home clash against Newcastle United in the Premier League.
The Gunners will be desperate to end their run of four consecutive league draws when they face the Magpies because only a run of victories will give them any chance of breaking into the European spots, and potentially even the top four.