The Gunners host Aston Villa in the fourth round on Sunday looking to lift morale following a third straight league defeat when they lost 2-1 at home to Manchester United last weekend, which saw them fall five points behind Chelsea.
Wenger, 62, has won the famous old trophy no fewer than four times since taking charge in 1996. The last came seven years ago, and there has been no silverware since.
The Arsenal manager, however, insists he would not take cup glory at Wembley in May ahead of securing another campaign in the Champions League.
"I have always told you exactly the same, the priority is be in the top four," said Wenger.
"In recent years I felt that we produced always the consistency at the top, top level and it is not enough for some people maybe, but for me that is the brand of a top level club - consistency in the top four."
Wenger continued: "I love the FA Cup, I think it is a top-level competition and I will always fight to win it.
"I won it four times and lost one final, and I don't know how many semi-finals. I always try to win every single competition.
"If you look at my record you will see the FA Cup is important for me. I think our record is better than all of them over the past 15 years.
"Even last year we went for four trophies. How many teams go for four trophies this season? Nobody.
"We always try to go for everything and for a long, long time last year we went for trophies late in the season, and still we will try to do the same and try to win the FA Cup."
French defender Laurent Koscielny may have only been in England for two years, but the world's oldest knockout competition has already left its mark.
He told the club's website: "I know in England that winning the FA Cup is a very big trophy for the team.
"We want to go as far as possible in this competition and so we have to win this game.
"It is important for the team because we have lost our last three games, and for the supporters because they were not happy after those defeats."
Arsenal have some of their defenders closing in on a return to fitness, with full-back Bacary Sagna - out since the defeat at Tottenham in October because of a broken fibula - having an outside chance of being included in the squad on Sunday. However, midfielder Jack Wilshere has suffered a setback in his planned return from ankle surgery.
Despite a packed treatment room, Wenger insists the answer is not just to go out and spend money.
"We played recently with 10 players out, to have only two or three out would help us a lot, much more than the transfer market," he said.
"You can look around at all the big clubs and who bought players? Nobody because you can't find players at the moment who can strengthen big clubs."
