The Gunners beat Newcastle 2-0 on Monday night to move ahead of Tottenham and Manchester United into third place in the Premier League table.
The last two seasons have seen Arsenal finish outside the top four and have to make do with Europa League football - reaching the semi-final last season and facing Napoli next week in the quarter-finals this time around.
After 19 successive years in the Champions League before their recent slip, Unai Emery replaced Arsene Wenger last summer tasked with taking the club back to Europe's elite club competition.
Goals from Aaron Ramsey and Alexandre Lacazette were enough to see off Newcastle and take Arsenal two points clear of neighbours Spurs.
Now Maitland-Niles, who made his Arsenal debut in a 2014 Champions League group game against Galatasaray but has not played in the competition since, is eyeing a return.
"It's every team's dream to play Champions League football," he said. "It's the best European competition in the world. To play against all the big teams would be fantastic and you get to test yourself fully.
"That's all we wanted to do, to go out there and win. We've made one step closer to succeeding."
Arsenal's rise has been rapid as they sat 10 points behind Spurs only a matter of weeks ago.
But, with Emery's side racking up points and Tottenham without a win in five league games, the tables have turned and Maitland-Niles admits seeing their north London rivals lose at Liverpool a day earlier provided motivation to get the job done against the Magpies.
"Yes, of course," he replied when asked if the Spurs result gave Arsenal extra incentive.
"I'm pretty sure everyone was at home watching the game last night. Everyone studied Newcastle too.
"It's just a good opportunity now for us to go out there, show our quality and say, 'look, we are one of the best teams in the league and we can compete for the Champions League once again'."
Newcastle remain 14th after losing at the Emirates Stadium but host Crystal Palace at the weekend looking for a sixth straight home league win.
Defender Paul Dummett believes beating the Eagles will all-but secure safety for Rafael Benitez's side as the Wales international targets a positive end to the season.
"We have been in good form at home with the wins we've had," he said.
"We know it is going to be a difficult game, they have got some really good players but we will be ready.
"We will work hard in training this week and hopefully we can get the sixth win, get ourselves safe in the Premier League and push on with some other good results to finish strongly like we did last season."
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