Villa travels to the Emirates Stadium after the north-London club knocked out Championship side Leeds United 1-0 thanks to a solitary Thierry Henry strike earlier in January, while Alex McLeish's team won 3-1 at Bristol Rovers.
Wenger has won the coveted trophy four times in his 15-year spell with the Gunners and the Frenchman believes his team always try to win every trophy they can.
“If you look at my record, you will see the FA Cup is important for me,” the coach told reporters on Friday. “If you look at the record of all the other teams, 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. I think we always try to go for everything and for a long, long time last year we went for trophies late in the season. Still we will try to do the same and try to win the FA Cup [this year].”
The Gunners boss admitted he is relieved to have defender Bacary Sagna back in training, while Mikel Arteta and Thierry Henry are set to be included in the matchday squad.
“Bacary Sagna is back in full training,” Wenger revealed. “Many players who are not specialist right backs have been playing in this position so we are relieved to have Bacary back. [Arteta] is very close to full training, Thierry Henry as well.”
Despite being short on natural left backs, Wenger denied the north London club is looking for a fresh face to bring in this transfer window and insisted the club will cope.
He said: “Gibbs is back in full training on Monday, and Vermaelen can [also] play left back and he is fit. [Andre] Santos will be fit in March.
“Three left backs, plus Sagna – who can play there – is four. We are not [shopping for a] left back.”
Alex Oxlade-Chamberlain was one of the top performers for Arsenal in its 2-1 defeat at home to Manchester United last Sunday, with Wenger's decision to replace him for Andrey Arshavin receiving much criticism and the French coach revealed the 18-year-old will be fit for Sunday.
“He is alright, it was just fatigue. His calf was not gone or anything like that, he just started to tire a little bit," he continued. “It is normal for a guy who plays a game at that intensity. But health-wise he has no problem. He will be involved on Sunday.”
After being jeered for bringing on the Russian attacker, the manager suffered more boos when the side conceded late and lost the match, but Wenger admitted the crowd reaction did not bother him too much.
“I can live with that. I do not think about the fans' reaction, I think about how we can win our games," said Wenger. “I will live forever by the values I think are right in football. One or two lost games, or one or two bad reactions will not change that.
“I always believe the fans' reaction depends on us. It is the team which has to get the fans behind them, and the fans have to be proud of the team. The vibes have to come from us.
“What was disappointing for me was that we produced a bad performance in the first half [against United], but a decent performance in the second half and should have won.
“We did not deserve to lose. The team did not get the credit it deserved for the performance in the second half.”Follow GOAL.COM USA on