The London club were reported to have agreed a fee for Italy striker Balotelli at the weekend, but Milan chief executive Adriano Galliani insisted that is not the case.
"Balotelli to Arsenal? We have not received any offer and at the moment there is nothing," he told reporters.
Wenger had been expected to bolster his forward line ahead of the new season, and he has already completed the signing of Alexis Sanchez from Barcelona.
And the Frenchman has now revealed that bringing in a goalkeeper and possibly a centre-back are his priorities for the remainder of the transfer window.
"It depends whether our midfielders get through now until the start of the season without injuries," said Wenger.
"Up front we don't need any more, maybe I will still bring in one centre-back. I will bring in a goalkeeper for sure and we are still out there to strengthen our squad.
"You do the deals when it's possible, this time we could do it early and I am very happy with what I have done until now. It’s easier to prepare, but we are not the only club who have done business.
"Some other clubs have also done business - Chelsea, Manchester United and Liverpool have bought great players and the competition should be interesting again next season."
