Arsene Wenger’s men have not won a major piece of silverware since lifting the FA Cup in 2005.
But they now top the table by four points and last weekend came through a potentially tricky away match last weekend with a 3-0 win at Cardiff, a match where Aaron Ramsey scored twice against his hometown club.
“We’re in a position that we’d like to be in for as long as possible,” Szczesny said.
“But it really doesn’t matter where we are now,” the Poland international added.
“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’s double in Cardiff gave him a tally of 15 goals this season for club and country.
The Wales international has been in scintillating form this season, having been nurtured back to physical and mental top form following a broken leg by veteran Arsenal boss Wenger.
“He has been outstanding until now,” Wenger said.
“You want always to jump into the future but we have to enjoy the present.”
The Frenchman 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.”
Meanwhile Manchester United striker Danny Welbeck urged the team to tighten up defensively if the champions were to close a nine-point gap on Arsenal.
They face manager David Moyes’s former club Everton at Old Trafford on Wednesday, having twice had to come from behind in last weekend’s 2-2 draw with Tottenham Hotspur.
“We gave away too many free-kicks which put us under pressure, so if we can limit ourselves from doing that, then I’m sure we will be a lot better in future games,” Welbeck told MUTV.
“Coming to White Hart Lane, we had the ability to come and win the game.
“That was on our mind but unfortunately we gave away two goals. Credit to us, we quickly got the goals back afterwards.
“We are a bit disappointed but we can be happy with a point at the moment.”
Chelsea have a potentially difficult trip to Sunderland while Manchester City will look to improve on a run of poor away results that could yet scupper their title hopes at West Brom.
Elsewhere, former Manchester United assistant manager Rene Meulensteen starts his reign as Fulham boss after replacing fellow Dutchman Martin Jol at home to Tottenham.
Fixtures (1945GMT unless stated)
Tuesday: Crystal Palace v West Ham
Wednesday: Arsenal v Hull, Fulham v Tottenham (2000GMT), Liverpool v Norwich, Manchester United v Everton, Southampton v Aston Villa, Stoke v Cardiff, Sunderland v Chelsea, Swansea v Newcastle, West Brom v Manchester City