The north London club have not won a trophy in eight seasons, though won eight of their last 10 games of the 2012-13 season to claim Champions League qualification for the 16th consecutive season.
And Ljungberg, who won two Premier League titles under Wenger, is adamant the club have what it takes to mount a title push next season, despite their ever-extending trophy drought.
|12/1||Arsenal are 12/1 with William Hill to win the Premier League
"I think it's extremely important that they qualified for the Champions League, otherwise it could be difficult to attract certain players. I always say that they are going to win the league so I'll say that again.
"The club went out after the game against Newcastle and said they weren't happy with being fourth. They want to win trophies as a club and I think that was a very important message they sent to all the fans."
Gunners boss Wenger managed to guide his side to fourth spot last season despite calls for his head, and Ljungberg believes he is the right man to take Arsenal forward and one of the very best coaches around.
"I think [Wenger] and Sir Alex Ferguson are the best managers in the world," Ljungberg added.
"He's done remarkably well for a very long period of time and I think with some certain economical restraints at times when they were building the stadium. To still achieve what he's done is actually quite remarkable."