The Spaniard, who is currently out injured with an ankle injury, has been linked with an Emirates Stadium exit with Goal.com UK exclusively revealing last week that Galatasaray are leading the chase for his signature.
“No [I won’t sign another goalkeeper] because we still have Vito Mannone who plays at Hull who is available,” Wenger told the official Arsenal website.
“I think Almunia will stay, then we have three goalkeepers. People want us to have four, five, six, I don’t know.
“We have a young Argentinean boy [Emilio Martinez] as well who is very good. We have plenty of goalkeepers, I think a club who works well can produce good goalkeepers.”
Vito Mannone recently extended his loan spell with Hull which will see him remain there until the end of the season and Wenger isn't sure if the club are even able to recall him.
“It is a complicated question to answer because I don’t think we are [able to],” he said.
“We had to make a decision at the time before we knew Almunia was going out or not. I didn’t want the problem of bringing Vito back and being No. 3 so we took the gamble. I think we can bring him back only in the case of exceptional injury.”
Meanwhile, Wenger is confident that centre-back Thomas Vermaelen will not need surgery but fears the Belgian will still be out for a long period with an Achilles injury.
“We don’t know yet, we don’t think so,” he added. “But he is still a while away yet.”
The Arsenal manager also believes that footballers should not be singled out due to their often high wage packets.
“Why would you just want to punish football?” he asked.
“There are plenty of people out there who make much more money than footballers. What you want is that every company is managed in a responsible way. That is the first step our society has to go.
“I don’t know why if a company makes a £50 million profit, people in the company shouldn’t be rewarded. That would mean only the owners would be rewarded, that would be unfair. People that work in the company have to get their share of the success of the company.
“In the whole of society if you want to limit wages, why not? That needs a complete debate and is more political than sporty.”