However, Wenger insists the club are working hard behind the scenes to acquire new players. Speaking to Sky Sports on the latest leg of Arsenal's preseason tour in Vietnam, Wenger said: "You want me to announce a spectacular signing, but I can't. We are working behind the scenes to strengthen the squad - but I can't give you names."
Over the next few slides, we count down Arsenal's top five transfer targets according to how badly Arsene Wenger wants to add them to his squad.
Arsenal need a defensive midfielder to partner Mikel Arteta. Arsene Wenger appears to have identified Bayer Leverkusen's Lars Bender as the man best placed to fill that void.
According to The Guardian, Arsenal have already had an £18.5 million bid for Bender's services rejected. The fact that Arsenal are prepared to break their transfer record to sign a relatively unheralded player shows just how highly Wenger rates the German midfielder.
The Gunners may well return with an improved bid between now and the end of the transfer window.
With Thomas Vermaelen sidelined with a back injury, Arsenal currently have just two senior centre-backs in Per Mertesacker and Laurent Koscielny.
With Johan Djourou having moved to the Bundesliga on loan, the next in line for a first-team spot is Spanish youngster Ignasi Miquel.
Arsene Wenger will be keen to improve his defensive options. According to Sky Sports, the Gunners are preparing to formalise their interest in Swansea skipper Ashley Williams.
Williams' intelligent passing game would fit well with the Arsenal style.
Arsenal's biggest priority this summer is acquiring a new striker.
United are not keen to sell, though, as David Moyes told Sky Sports:
Overall, my thought on Wayne is, if for any reasons we had an injury to Robin van Persie, we'll need him.
Wayne can play up on his own, he can play dropped in. It's going to be a time to see how I work with Wayne.
Manchester United isn't about Wayne Rooney. Manchester United is about the team - the club.
Moyes' words were intended to reassure Rooney. However, suggesting he is merely a backup to Robin van Persie may have riled the England centre-forward.
If Rooney insists on leaving, Arsenal will be waiting to pounce.
Arsenal's interest in Gonzalo Higuain is long-standing and well-documented.
However, the latest from The Daily Mail suggests that Arsenal's move for the Argentine striker may now be in jeopardy. The Real Madrid man was set to meet with his club president yesterday to discuss the possibility of remaining at the Santiago Bernabeu next season.
Higuain seems like a more realistic target than Wayne Rooney, although if Real play hardball, Arsenal will have to stump up a lot of cash to get their man.
It sounds incredible, yet Liverpool's Luis Suarez is emerging as Arsenal's top transfer target this summer.
I’ve heard him say it would great to have an opportunity to play for Arsenal and likewise Real Madrid. But he certainly hasn’t called me up and said he wants to leave.
We had an offer which is fairly public from Arsenal. We said "no" to that offer, and as far as we’re concerned he turns up for training when he’s due back, and we’ll move forward on that basis.
According to The Guardian, Arsenal are preparing to launch a new £35 million bid for Suarez.
If Arsenal are prepared to double their transfer record, Suarez simply must be Arsene Wenger's preferred signing.