The North London club lifted the title back in 2004 while their last silverware came seven years ago winning the FA Cup.
Cash-rich clubs such as Chelsea and Manchester City have achieved success previously while Manchester United have also been successful with high-profile signings in the past. However, Arsenal have been criticised for not spending sufficiently during the transfer window.
But according to Wenger, not being able to spend like their rivals doesn't mean they can't dream of lifting the title.
"Firstly, I must say that not being able to match the spending of the richest clubs does not mean that you can't compete with them on the pitch," Wenger was quoted as saying in DailyMail.
"The Chelseas and the Man Citys are new problems. But with this new financial environment, what has not changed at all is our policy that we will be as ambitious as ever and spend the money that we have available, if possible in an intelligent and wise way," Wenger said.
Under Wenger several stars made their mark not only in England but all over Europe and the rest of the world.
"We have always spent money because we are ambitious for top-class players and if you look at the history of our last 15 years, we have always had top-class players," Wenger said.
"It does not mean you can't win the title if you can't compete financially," he added.
Arsenal have added more striker force with the signing of French striker Oliver Giroud and Germany winger Lukas Podolski. But Wenger feels spending money should not be any clubs target.
"I have been in football for a long, long time and I don't think just spending money is a target that is defendable."
"To spend the money on a top player is defendable. But just to spend the money is like you are worried," he said.
Wenger insisted Gunners' fans should be proud of the way the club has developed over a short period of time.
"Our fans can be proud of the way we run this club, of the quality of the players we have and of the financial situation that is existing at the club," Wenger said.
"Rather than convicting this club, they have more reason to be proud of the whole situation here. We have built a team and a stadium in such a short space of time, and have a strong financial situation - and we have always survived at the top level," he said.
Wenger feels the introduction of Financial Fair Play can have a positive impact on the club and the league.
"We need first to see how effectively financial fair play can be enforced before we can fully understand the impact but I believe it will make for a more exciting Premier League," Wenger said.
"If that is possible again it will be even more interesting".
"I don't want to go into excuses but you want a business to be run properly and I believe that to lose £150million a year, you don't deserve a lot of credit to win a competition," Wenger said.
"I think that it is right that you balance your books - to accept the one basic principle for every company - and that's that you can spend the money which you make. That principle just seems to be a common sense and logical one," he said.