The north London club produced their latest impressive display in beating Cardiff 3-0 on Saturday, with in-form midfielder Aaron Ramsey grabbing a brace against his boyhood club.
The win moved Arsenal seven points clear at the top of the table, although Chelsea subsequently trimmed the advantage back down to four by beating Southampton on Sunday.
Arsenal have not won silverware since their FA Cup triumph in 2005, while their last league title came in 2004.
Goalkeeper Szczesny knows there is still a long way to go with only a third of the season completed, but feels Arsenal will win the title if they can maintain their current level of performance.
"We're in a position that we'd like to be in for as long as possible," he said. "But it really doesn't matter where we are now. It matters where we are in May, and if we carry on like we are now then I'm certain we'll be top in May.
"But we have a lot of work to do, a lot of tough games to win. There's no point in putting pressure on ourselves. We just want to enjoy every single game, that's bringing the best out of us and I don't think that will change."
Ramsey and Mesut Ozil have been the driving forces behind Arsenal's excellent recovery from the opening-day loss to Aston Villa.
The brace at Cardiff took Ramsey's tally to 15 goals for club and country this season, and underlined the Gunners' title credentials on a ground where Manchester City, Manchester United and Everton have all dropped points this season.
The calibre of Ramsey's displays make him arguably the form player in the top flight this term, and Wenger believes he would be named player of the year if a vote were taken now.
But the Frenchman also admits he will need to make sure he does not over-use the Wales international.
He said: "He has been outstanding until now. You want always to jump into the future but we have to enjoy the present.
"If he keeps playing like that, of course (he will be player of the year), but it has only been a third of the season."
He added: "I have to treat him like the other players and give him a breather when he needs it. I want him to continue to develop, but he is so young you imagine why should he stop his development now?
"Let's not forget that one year ago everyone questioned him. That shows you that he deserves credit for that - he has turned a corner and he can continue to improve."
When asked if he felt Ramsey was currently the best player in the Premier League, Szczesny added: "I don't think there's a need for us to make such statements, but I imagine he does pretty well at Fantasy Football!
"We're so pleased for him. He's been through a lot, he's come back so well and I just hope he continues. Is he the best in the league? I don't care as long as he does the job for the team.
"I'm just as amazed as everyone else. We always knew that he could play well but to score as many as he has, any striker would be delighted with that. He's been so good."
Source: PA
Source: PA