The Gunners have been stuck in a transfer merry-go-round trying to sign the Gabon international.
After seeing their first two offers knocked back, Arsenal finally agreed on a £55.5million fee with Borussia Dortmund.
It is believed the Gunners are waiting for Olivier Giroud to join Chelsea before Aubaeyang’s move to north London is authorised.
The 28-year-old was at Arsenal’s training complex on Tuesday completing the formalities ahead of the switch, having flown to the capital from Dortmund that morning.
And when Wenger was asked when the deal will be completed, he said: “We will know about that tomorrow morning.
Meanwhile, the Gunners suffered a setback on the pitch as they lost 3-1 to Swansea.
Nacho Monreal put the visitors 1-0 up but a Jordan Ayew strike, sandwiched by a Sam Clucas brace, dropped to Gunners to eight points outside of the top four.
“I felt defensively we were very poor and made big mistakes,” Wenger said after the game.
“It’s better not to talk about the second or third goals.
“Swansea were sharp, disciplined and hungry. Unfortunately I believe we were not good enough, I believe we were not disciplined enough.
“I don’t want to talk about second or third goals.”
As for Giroud, who came on as a substitute at the Liberty Stadium, Wenger said: “It’s a possibility (he will leave)”.
“But all that will be decided tomorrow morning.
“We will inform you once that is more definite.”