The Saints will take on Arsenal at the Emirates tonight in their Capital One Cup opener.
Many tipped Southampton to struggle this season after a mass exodus of first-team players in the summer, but manager Ronald Koeman has guided his side to three wins out of five in the Premier League.
"Why can't Southampton win a cup this season? Anything is possible," Schneiderlin told reporters. "We're going to go to Arsenal, play our game and do the best we can.
"The players at this club want to do something great in the cup, it's very important to us. It's the shortest way to get into the Europa League, which would be great for the club and for the fans."
Southampton have beaten Arsenal in North London just twice in their history.