The Gunners head into the final game of what has been an extraordinary Barclays Premier League campaign with destiny somehow still in their own hands.
Arsenal opened the door to their rivals in the battle to secure automatic Champions League football following a thrilling 3-3 draw with Norwich at Emirates Stadium last Saturday.
However, in the wake of Newcastle's home defeat by Manchester City and Spurs draw at Aston Villa on Sunday, it is Wenger's men who remain in the driving seat, one point ahead and with a better goal difference.
The Gunners boss, however, insists he will not have one ear on what is happening at White Hart Lane or Goodison Park as his team aim to make every other result redundant by beating the Baggies in Roy Hodgson's final game before he takes over at England.
"It can happen that we will have to look, but normally I never do that. We want to win our game and if we do that we don't need to listen to anybody," Wenger said.
"I was [deflated after the Norwich game] because it was the first time in a long while that we did not have our fate in our own hands. You don't like that to happen.
"With the results we made on Saturday, that is what happened and in fact the other teams did not take advantage of it.
"That is why it is back in our hands and of course it is a big lift for us, because for a long time [earlier in the season] it was not."
Wenger, though, accepts Arsenal cannot afford any more defensive frailties like they displayed against the Canaries, who were 1-0 down after 65 seconds but went on to lead at half-time and then snatched a point through Steve Morison's late equaliser after Robin van Persie's brace had turned the match around.
"We were focused and switched on in the last couple of weeks," the Gunners boss said.
"At Stoke we had a good game and offensively against Norwich we had a good game. Defensively, though, we had not the expected level.
"Maybe we were focused too much on winning the game and forgot that to win the game you need to defend as well."
Should Arsenal fail to produce the required result on Sunday, they could end up in fourth place or indeed fifth if Newcastle, who are two points adrift, win and they lose.
Failing to secure third would leave an anxious wait to see if Chelsea win the Champions League final in Munich, which would mean the Blues take the place in the group stages next season with the fourth-placed Premier League side dropping down into the Europa League rather than go into the qualifiers.
Wenger, though, will not concern himself with that possibility.
"The rules are the rules, you know them at the start of the season and you have to accept them," he said.
"I believe we want to finish third, we have the potential and the possibility to do it, so let's do it.
"The consequences of if you don't do it, you deal with that after the game.
"You look at it as an opportunity you want to take, and that is what we want to do."
That Arsenal are even in this position given their appalling start is an achievement in itself, and one few would have predicted following four defeats from the opening seven Premier League games as the Gunners slumped down to 17th.
Defender Laurent Koscielny admitted it had been a "catastrophic" start, but one from which the Gunners deserve credit to have recovered.
In an interview with France Football, translated on www.arsenal.com, the centre-back said: "We had to put the house back in order, and everyone did their bit: the coach, the club, because we were in a critical situation.
"The squad wasn't giving enough for the club, and was aware of it.
"We got back to work, we told each other the things that needed to be told; after which, one win, two wins, confidence comes back, and things follow from then on.
"The new players gelled in the squad, and here we are."