However, Wenger believes that the Gunners, who are currently in third place, can challenge Manchester City for the second spot on the table.
With nine games left in the season, many people, including Chelsea head coach Jose Mourinho, feel that Arsenal have the opportunity to taste Premier League glory. But, Wenger believes that this is highly unlikely to happen.
"We would love to be in it [the title race], but at the moment we are too far away from Chelsea," he said. "Every week we have a chance to get closer.
"We need positive results and negative results from Chelsea because, at the moment, they have a very good cushion and very good security. What we can master is positive results from us.
"They [Chelsea] still have a game in hand and they are too far away at the moment. They suffered a little in the first half [of a 1-1 draw against Southampton last Sunday], but in the second half they could have won the game."
Wenger also believes that numerous teams are in contention for a top four finish this season.
Arsenal will be looking to cement their position in the top four when they travel to Newcastle on Saturday.
"It is very tight," Wenger said. "We are on the neck of Man City, and straight behind us we have Manchester United, Liverpool… even Tottenham and Southampton are not completely out of it.
"It's down to our performances between now and the end of the season. I do not sit and think second is good. I look at what is the best possible team to win this game at Newcastle."
The Gunners saw their Champions League run ended by Monaco on Tuesday, but they still have the opportunity to finish in the top four and retain the FA Cup.
"I let other people have that assessment [of what constitutes a successful season]," Wenger said of his side's situation. "My job is to win as many games as I can. I leave assessment for the quality of our performances to specialists who have to assess that.
"Our mood is down and disappointed [after the Monaco result]. As well, it is quite strange at the moment because we feel we are on a positive trend and we hate to be out.
"Basically, we paid for the fact that this was a game of 180 minutes and, in the first 90, we were not cautious enough defensively.
"Now we focus on our next targets. First of all, we get back into the Champions League. Then continue to improve. We are a better team today than four months ago, and we have to keep that attitude.
"We have won 13 of our last 15 games, and that's down to consistency, our quality and our improvement. Now we have to push on until the end of the season.
"We are in the semifinal of the FA Cup, and in a strong fight in the Premier League. It is important to focus on these targets."