"We have a great squad here and we are still capable of winning it. The year before we did it with basically the same squad.
"And maybe we didn't need to spend that much - after all, we have Jermaine Pennant, Ryan Garry and David Bentley coming through. Hopefully, Jermaine will get his chance."
Cole, of course, could also face competition for his England place from Wayne Bridge. Chelsea's £7m signing from Southampton says he hopes that if the Blues qualify for the Champions League group stage he will be able to put pressure on Cole.
Bridge said: "Ashley has done superbly in that position but hopefully, with me coming to a bigger club, I can push him a bit harder."
Cole is candid about the disappointment of missing out on the title. He said: "It killed the summer for me in many ways. But it also served to give me and the rest of the squad a new desire and hunger to win it back."
Cole believes some of the younger players could be key - especially Pennant, who embarrassed his club after going AWOL while on England Under-21 duty. Wenger stood by him and Pennant has responded in the right fashion.
Cole said: "He has grown up from it. He sat down with the manager and had a good talk and Jermaine said he was going to knuckle down and prove he can play.
"He did well on our recent tour to Austria and is training really hard. It is good for me and Arsenal to see."
Thierry Henry, Sylvain Wiltord and Robert Pires will not feature tonight, as after playing for France in this summer's Confederations Cup Arsene Wenger is still building up their fitness.
Dennis Bergkamp may play but Martin Keown (groin) will not and, according to the manager, Sunday's Community Shield against Manchester United will be "too early" for the centre back.
"We have small things [from the Celtic match on Saturday] because it was a physical game," Wenger added. "Freddie [Ljungberg] and Jermaine Pennant have done their ankles a bit while Martin Keown has a small problem. But there's nothing major."
