Last summer was a mess as far as the transfer market was concerned, saved by the last hour signing of Mesut Ozil on deadline day.
Yet they still failed to sign a major striker, and in the eyes of many, this let them down in the title race last season.
Wenger last week agreed a new three-year deal to remain at the club, and buoyed by FA Cup success, he feels confident the club are en route to adding more silverware.
However given the way the club left their transfer dealings until the last minute last summer, Wenger is adamant business is going to be done imminently, stating this month and next would be the big ones.
He told Arsenal.com: "We know we have to… have a successful June and July, that's where you strengthen the team."
Last summer by time the season had begun in August, Arsenal were still scratching around for signings, and the worried mood at the club illustrated in their opening day 3-1 loss to Aston Villa.
A year before, Arsenal's summer was ruined by Robin van Persie's August departure, but this year there are no integral squad members likely to be leaving save for Bacary Sagna who has already confirmed he won't be re-joining.
Wenger appears confident he will get the job done this summer, and early, hinting he already has an inside track when it comes to players he wants to sign.
"What I can promise is that we work very hard on a market that is very, very congested with many people who have a lot of money.
"But we have a big advantage, players want to join us and if we find the right quality I'm sure we can strengthen the team."
Whether he was talking about any players specifically or not, his comments bode well and if Arsenal's negotiating team can get their bids right, the Gunners may have a few new additions in time for their pre-season tour.