Arsenal head to St James' Park on Sunday one point clear of north London rivals Tottenham following their 4-1 win over Wigan, which sent the FA Cup winners down.
Europa League champions Chelsea are two points ahead, but the statistics are so close that should Arsenal win by a two-goal margin and the Blues slip up at home to Everton, then Wenger's men would jump into third place and earn automatic entry into next season's group stages.
However, should the Gunners win 2-1 at Newcastle and Chelsea draw 0-0, then the two London clubs would be tied and, under Premier League rules, an extraordinary play-off would have to be played.
Wenger, though, accepts if his men fail to win at St James' Park, then that scenario would be redundant.
"I would fancy that," said the Arsenal manager.
"A play-off exists only if we win the game [at Newcastle], so let's win the game and see what happens.
"The biggest task is to win the game and not speculate too much on what happens after because the first compulsory thing we face is to win the game on Sunday."
Arsenal edged out Tottenham on the final day 12 months ago to snatch third, and history could be set to repeat itself this weekend.
"I know for a long time that for us, when we were seven points behind, we would all be happy that it goes to the last day," said Wenger.
"We are in a position where nobody expected us to be. We have our destiny in our hands, our fate in our hands and that's what you fight for in the game.
"It is a game that we will now want to win but at least we fought back to be in a position where we master our own fate."
Wenger also paid tribute to David Beckham and admitted that he had been interested in signing the midfielder - but could not afford to pay his wages.
Beckham, who announced his retirement, had spells training with Arsenal but never played for the Gunners.
Wenger said: "I have a huge respect for his passion for the game, his huge commitment, his mental strengths because he was under a lot of pressure throughout his career, and his dedication. I think that is where he is an example."
Asked if he had ever been interested in signing him, Wenger added: "Yes I was, but it was at the period where we could not afford to pay him."