Jurgen Klopp's side reached the final of Europe's premier competition last term, losing 3-1 to Real Madrid in Kiev, and they are level on 23 points with leaders Manchester City after nine games in England's top flight this time around.
That setback came in the aftermath of back-to-back domestic meetings against Chelsea and ahead of a goalless draw with City, but England right-back Alexander-Arnold is confident Liverpool have the squad depth to cope with such demanding periods.
"I wouldn't say there's a standout one," he told a pre-match news conference when asked whether success in the Premier League or Champions League is preferable.
"We're a good enough squad to be challenging for both. We're not going to rule one out or put one to the side.
"They're both as important as each other. It's hard to pick one, so I'd say both."
Liverpool have made a marked defensive improvement in the Premier League, with their backline breached only three times so far in the current campaign.
They have conceded 13 goals in the six outings since their last Champions League clean sheet but Alexander Arnold is not overly concerned.
"We want to concede as little as possible, but we still got to a Champions League final and we've got a few points in this campaign, so we're not in the worst position possible," he added.
"We're still getting wins, and the three points are the most important thing. We know there's still a lot to give and always room for improvement.
"That's something we're all excited about. We need to strive towards getting better, putting in better performances and getting towards our full potential."