Recent form suggests the Swans may be in with a chance, after victories over Newcastle at St James' Park and a 3-1 win over high-flying West Brom in midweek.
And ex-Arsenal trainee Britton knows that a win over his former side on Saturday will take them above the Gunners and closer to their dream of Champions League football next season.
"If we win on Saturday we go above Arsenal and then we'll start looking at the top four," Britton told BBC Sport.
"It's great going to Arsenal and they're one place above us.
|SWANS SOAR OVER EUROPE
|300/1||Swansea are 300/1 with Bet365 to finish in the top four this season|
"It's been a good start but there's still a long way to go, but we'll go to Arsenal and it's a great place to play football.
"You can go there with a little bit of pressure off but at the same time we want to try and put a performance on and come away with something. We don't want to turn up and make the numbers up."
Swansea manager Michael Laudrup hailed the 3-1 win over West Brom as "the best performance he has seen for several seasons", and Britton believes the attacking football played under the Dane is paying off.
"It's arguably our best performance, the [opening] 45 minutes anyway. It was great to play in," he added.
"Everything seemed to be going for us in the first half. We kept the ball well, we had a lot of chances and everything just seemed to click. There's more goals in the team.
"The only disappointment was conceding just before half-time.
"We're a bit more attacking. Obviously at the same time you can leave yourself open but it's a bit more attacking football so you're going to have that."