The former Gunners forward believes Arsene Wenger may miss out on potential transfers if they are also being targeted by the Premier League's elite.
Wright believes the appointments of David Moyes at Manchester United and Jose Mourinho at Chelsea, coupled with Manchester City's resurgence under Manuel Pellegrini and Tottenham's attempts to improve this summer, may make it a difficult transfer market for Arsenal.
"Arsene Wenger’s future at the club is secure, because he has done so much for the club since he got there," said Wright, who was speaking at a charity event at the Marina Bay Sands resort in Singapore. "I feel that the quality of signings over the past few years is the reason why they haven’t won anything in eight years.
"They have to sign players with the right qualities, but they are going into a team to help young players who are coming through.
"I think it’s going to be harder for Arsenal because Manchester United has a new manager, and so do Chelsea," he warned. "Manchester City have a point to prove, and even Tottenham are coming through. It’s going to be hard to try to attract the kind of players that’s not going to want to go to those other clubs."