The Gunners are the only English side to win the competition, and they travel to Italy to face Fiorentina in the first leg of their knockout tie.
Two-time semi-finalists City start in Switzerland against amateurs Lugano.
“We definitely want to win it and know we can,” said forward Janine Beckie.
“Winning the league is important, that is a huge one for us, and we would love to repeat on the FA Cup and Continental Cup, but now we have that opportunity for a fourth trophy and that is something only two teams in England can say.”
As WSL champions, Arsenal are one of them for the first time since reaching the quarter-finals in 2014, when they were knocked out by English rivals Birmingham City.
Both they and City enter the competition at the round of 32 stage alongside Glasgow City, who face a trip to Russia to face Chertanovo, while fellow Scottish club Hibernian came through qualifying to set up a meeting Czech side Slavia Prague.
‘Gunners feel the vibe of Europe again’
The trip to Florence and the return leg in London two weeks later are part of a busy opening three weeks of the season that see Arsenal in action six times across three competitions.
England midfielder Jordan Nobbs, who returned from a long-term knee injury in Sunday’s win against West Ham, believes it is a “good time for players to step up”.
She told BBC Sport: “We want to win more trophies this year so we need a squad to do that.
“I’d like to say we’d get to a point where we can go on and win it, but we have to take each game as it comes and believe every single time we go onto that pitch that we can keep getting through the knockout stages.”
It is the second year in a row that Fiorentina have come up against a side from England’s capital, with the Italians last season going out 7-0 on aggregate to eventual semi-finalists Chelsea.
‘City motivated by early exit’
Manchester City, who were eliminated in the opening round last season by Atletico Madrid after reaching the semi-finals in the two previous campaigns, will be the first side Lugano have faced in the Champions League.
Canada international Beckie said the tie poses a “big wildcard” but they have “done their research”.
The striker, who is yet to play in the competition having been an unused substitute in the first leg last season before missing the second because of international duty, said their early elimination 12 months ago has galvanised the side.
“It didn’t stain the season but it was disappointing and it is definitely motivation to not let that happen again this year,” Beckie told BBC Sport.
“We had great year last year, two trophies was more than anyone in England could say. But I think we have a group of girls that can really push in the Champions League.
“Part of the reason I moved here is so I could play Champions League. It is an exciting time in my career and hopefully we can have some success.”
In a week that Nick Cushing’s City side smashed the record for the biggest WSL crowd, with more than 31,000 watching them triumph against Manchester United at the Etihad Stadium on Saturday, Beckie said no-one has been distracted from what is being demanded on the pitch.
“It was a great occasion, a memorable and historic game for the club that a lot of us will remember for a long time,” she added.
“The girls did a good job managing the emotions of a big game like that.”
“From our performance there are a lot of things that we would like to do better and work on for out next game, and this is our goal.
“We just want to win and believe we are a team that should win and dominate teams – that is our mindset.”
Additional reporting by Emma Sanders