Arsenal have not won the Premier League since 2003-04 but with the acquisition of Alexis Sanchez, plus their victories in the FA Cup and Community Shield, Winterburn said there is a positive mood around the Emirates ahead of the new campaign.
The London-based club defeated reigning Premier League champions Manchester City 3-0 on Sunday to win the Community Shield at Wembley, with Santi Cazorla, Aaron Ramsey and Olivier Giroud scoring the goals.
And Winterburn claimed on Wednesday that the signing of Sanchez, just a year after they bought Mesut Ozil, shows Arsenal are a 'buying' club again, rather than a 'selling' club.
"Whereas the last three or four years, Arsenal have lost their top players, which was never heard of when Arsene Wenger first came," Winterburn told Perform.
"He only sold his top players when he thought that they were past their peak, and then they started to lose (Cesc) Fabregas, (Samir) Nasri, (Robin) van Persie, and that's the wrong statement that's being sent out to the other players, and also to the supporters.
"All of a sudden, in the space of a year, we started to bring in some big players, FA Cup is won as well. That gives you a good feel good factor if you like, and maybe makes the supporters believe that the club is starting to move in the right direction again which is what I actually believe."
But Winterburn, who won the 1997-98 Premier League with Arsenal, remains well aware of how hard it will be for Wenger and his men to overcome the likes of City, Chelsea and Liverpool through the course of the season.
"The league is now so hard to win, it's so competitive," the former left-back said.
"You've got five or six teams realistically that can put together a decent run to win that title so it is harder but Arsene Wenger will now believe that at least he can stop people talking about nine years since a trophy."
