The Gunners head into the New Year as leaders of the Premier League, with some of their title rivals tipped to spend heavily as they enter the second half of a fiercely contested title race.
Arsenal have stayed in the hunt, despite limited attacking options which have forced Olivier Giroud to shoulder much of the workload as a sole striker.
Wenger tried to add more firepower in the summer, but failed to lure Suarez from Liverpool and will not make another attempt to prise away the Uruguay international, who signed a new deal at Anfield this month.
But he is looking for another big-name player to bolster his side following the marquee signing of Mesut Ozil in the summer.
"We are as many clubs, certainly on alert," said the Frenchman. "If something special turns up, we will not turn it down.
"But we are not as well desperate because we have a big depth in our squad. We have shown that because our midfield for example at West Ham and at Newcastle was completely different. We changed three players and we still managed to have a very strong team."
When asked if he had given up hope of signing Suarez, Wenger said: "Yes of course. There won't be any approach, no."
An injury to Yaya Sanogo has denied Wenger another attacker, but a fully-fit Nicklas Bendtner and the return from injury of Lukas Podolski have given him fresh choices up front.
"At the start we gambled on Sanogo, who has been injured until now and I thought that he could come in for some games and help us, but of course he has not been fit at all," said Wenger.
"Nobody knows what will happen because Bendtner is coming back in good shape now. Podolski is back, so we have a bit more choice up front."