But all their eggs are now in one basket as they seek to end their trophy drought, with leaders Liverpool almost out of sight in the Premier League.
Arsenal, who have never been crowned European champions, have become used to battling for the English league title - narrowly losing out to Manchester City in the past two seasons.
This year it has been their misfortune to be competing against a Liverpool team that flew out of the blocks in Arne Slot's first season at Anfield.
Arsenal have had chances to put the pressure on the runaway leaders but 12 draws in the Premier League, and just two wins in their past seven games, have cost them.
Saturday's 1-1 draw at home to mid-table Brentford meant the Gunners finished the weekend 13 points behind Liverpool, who could wrap up a record-equalling 20th English league title as early as next weekend.
Arteta denied that his players had been distracted by their upcoming match in Spain but his team selection showed where his priorities lie in the final weeks of the season.
The Spaniard made five changes to the side that beat Real, with winger Bukayo Saka and captain Martin Odegaard left out of the starting line-up.
Afterwards, he turned his attentions to Real.
"We still have six games to play in the Premier League, which are going to be really important, for sure," he said.
"But, for now, it's all about Wednesday."
Arsenal will travel to Madrid in high spirits, even though the 15-time European champions regularly defy logic in the competition, meaning Arteta will not breathe easily until the final whistle.
Even if the Gunners do make it through, Paris Saint-Germain and Barcelona - both hugely impressive - are also expected to progress to the semi-finals.
Arsenal's high-wire act means they risk ending the season without major silverware for a fifth straight season despite the undoubted progress made under Arteta.
And the Gunners' hold on second place in the Premier League is by no means secure.
They are six points above a faltering Nottingham Forest.
Newcastle United, in fourth spot, are seven points behind but have a game in hand and are in a rich vein of form.
Arteta said after the Brentford draw that the club were disappointed to find themselves so far adrift of Liverpool.
"It is difficult because obviously there are a lot of reasons why we are with that distance (to Liverpool in the Premier League) and the amount of things that we have to deal with and still we are where we but yeah, we want to be higher, that's for sure," he said.
Despite their stumbles, Arsenal are almost certain to secure one of the five qualification places for next season's Champions League.
But slipping below second would dent the Gunners' pride and challenge the perception that they are making relentless progress towards their first Premier League title since 2004.
Arteta still has the rest of this season to think about even as he starts plotting how to strengthen for the 2025/26 campaign.
The Gunners could make club history in Europe in the next few weeks but if they fall short, the season could end with a whimper.
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