Ranked third in the world, Sweden are traditionally a superpower in the women's game but their only triumph at a major tournament came at the 1984 European Championship.
They reached last year's Euro semi-finals, lost the Olympic gold to Canada on penalties at 2020 Tokyo Games and were third at the 2019 World Cup. Their best finish at the global soccer showpiece was in 2003, when they were runners-up.
"Sweden is always a contender, I would say," Asllani told reporters on Saturday. "It's not only because we are very highly ranked in world rankings, because at the end of the day that doesn't matter at all.
"But it's the way that we approach matches and tournaments, more and more players that got experience from tournaments and were more comfortable being a favourite in a sense like we've been before as well.
"Primarily, the way in which we approach this as a team, we have plenty of players with excellent qualities. Right now, I'm just dying to get out there and show people what we've been practising in the past couple of weeks."
Asllani will captain Sweden in their Group G opener in Wellington on Sunday, coach Peter Gerhardsson said.
Regular skipper Caroline Seger trained on Saturday but will start against South Africa on the bench, Gerhardsson said. The 38-year-old midfielder was included 23-player squad despite a lengthy struggle to overcome a stubborn calf problem.
"I love taking responsibility on the pitch and enjoy being involved both on and off it," Asllani said. "I think we have an incredible number of players who have leadership qualities.
"So for us it's never really been a question of who wears the captain's armband. We complement each other."