The Gunners have seen their squad decimated by injuries, with England midfielder Jack Wilshere ruled out for three months after ankle surgery earlier this week and captain Mikel Arteta set to be sidelined by a calf problem.
Wenger revealed at the club's AGM in October they would try to "rectify" their defensive options when the transfer window re-opens, and have been linked with a move for Aston Villa's Ron Vlaar.
However, the Arsenal boss insists bringing in any new player is not a matter of just simply writing out a cheque and shaking hands.
"You have to give us time
We do our job as always
This season we bought five players who are all top quality, so I think we have done really well on the transfer market and we try to repeat that in January," said Wenger, whose side will look to build on the midweek Champions League win over Borussia Dortmund when they travel to West Brom for Saturday's lunchtime Barclays Premier League kick-off.
"However, to buy football players is not like you go into a supermarket and just say: 'I want to buy a right-back or a centre-back.' It is to find the right quality.
"If you go out tomorrow you will see that everybody looks for the same positions everywhere, so it is not as simple as it looks.
"In January it makes it even more difficult because players are even less available than in June or July, but we will try to be creative and have one or two good ideas."
Wenger claims the scouting process "never stops now", but stressed that was across all the leading clubs.
"I always have lists that you read," he said.
"You come in on Monday, someone has seen a player and you have to follow up, watch him again, then watch him again and someone else has to watch him
Then when you come to conclusion that I have to watch him, so it takes time so that work never stops.
"But I can get on a case with a player who has a buy-out clause, you watch him one time and think: 'oh, that's really special', then the next day, the guy has gone to Real Madrid."
Laurent Koscielny is expected to return from his Achilles problem at The Hawthorns.
With France full-back Mathieu Debuchy expected back before Christmas from a serious ankle injury, Wenger feels he will have plenty of defensive cover and has been impressed with Spain international Monreal's switch into the middle alongside Per Mertesacker.
"He is playing very well, he doesn't get enough credit because against Manchester United, against Dortmund, he was in the top three for me with the quality of his performance," said Wenger.
"I tested him (at centre-back) before the season started in the Emirates Cup tournament and I could see that he understands and reads the game well
It is the most important quality in this position.
"Of course, after that there is the question mark 'can he cope with the physicality of this job?' because he does not have a major frame, but game by game, he becomes more aggressive because he understands the game, he can get in front of people and that is a very important quality."
Wenger added: "Monreal is committed
He has an excellent mentality, excellent attitude, top class, I must say every day he is focused, doesn't talk too much and does his job.
"He wants to do well for the team
I think he enjoys it more and more and you could see against Dortmund that now he is starting to get into it."
Source : PA
Source: PA