Pep Guardiola’s side have made their way to the quarter-final stage, where a meeting with Premier League rivals Middlesbrough awaits.
Were they to make it over that hurdle, then a day out at Wembley in the last four would be secured.
City’s sights would then be firmly locked on major silverware, with the club having last lifted the trophy back in 2011.
Sane believes a six-year barren run in the competition can be ended this term, with the FA Cup a more realistic target than the Premier League and Champions League crowns.
He told the club’s official website: “I think all of our players want to win trophies and the FA Cup will be the quickest route.
“Of all the three trophies we can win, perhaps the FA Cup is the easiest and that is why I think we have a good chance.”
Sane will be looking to provide cup inspiration for City against Boro, with the Germany international having come into his own over recent weeks.
The 21-year-old was snapped up for big money last summer and, having netted three times in his last four appearances, is starting to repay that faith as he continues to develop and mature under the guidance of Guardiola.
He added: “I am happy to have made the move to Manchester City.
“It's been great fun working with Pep Guardiola because you can learn a huge amount from him and I have already learned a lot.
“Also he’s very ambitious and wants to win all the time and wants to improve every player.”
Sane now has six goals for the season in all competitions, with 23 appearances made so far in his debut campaign at the Etihad Stadium.