Wenger's side have been eliminated from the Champions League and FA Cup in the last week and are on a run of one win in eight games in all competitions.
They travel to Goodison Park to face Everton on Saturday and, if results go against them, the Gunners could be 14 points adrift of leaders Leicester.
The worst-case scenario for Arsenal boss Wenger would be wins for both Manchester City and West Ham, which could see the north Londoners drop out of the top four altogether.
Wenger has never finished outside the top four in his 20-year reign, but the Frenchman admits it is a real possibility this time and he is keeping a close eye on the chasing pack.
"Yes of course. It's very tight. The Premier League is far from over but we have to look behind us because things can change very quickly," Wenger said.
"We want to move forward, but I'm conscious that our position is not secure.
"We have to take care of our own destiny and that's by producing the performances we expect from ourselves.
"We are in a position where we hope for the best. I agree that a negative result (at Everton) would be very bad for us."
Leicester have been warned that their fairytale challenge for the Premier League crown could be shattered by title wreckers Crystal Palace.
With only eight matches remaining, Claudio Ranieri's side are on the brink of arguably the most unexpected title triumph in English football history after establishing a five-point lead over second placed Tottenham.
The unheralded Foxes have defied all expectations to remain at the top of the table while their supposed superior rivals have struggled to keep pace.
But Palace manager Alan Pardew believes that wobble could come at Selhurst Park this weekend as the hosts aim to reprise their role as notorious party crashers.
In May 2014, Palace famously ruined Liverpool's bid for a first English title since 1990 when they fought back from three goals down to draw 3-3 at Selhurst Park in a result that effectively gifted the trophy to Manchester City.
Then last April, Pardew's men defeated City 2-1 in south London to all but end their hopes of overhauling eventual champions Chelsea.
"Human instinct is when you're trying to achieve something magnificent like Leicester are, you're going to start worrying and doubting," Pardew said.
"It's been almost the perfect season for them but it doesn't always come all the way through, that perfect run. Maybe their blips are still to come
"It has been a banana skin, this place, in the past and it's typical of Crystal Palace. Our history is littered with upsets against the odds."
If Leicester can extend their lead, it will put pressure on Tottenham, chasing a first title since 1961, to beat Bournemouth at White Hart Lane on Sunday.
Tottenham bowed out of the Europa League against Borussia Dortmund on Thursday but, with the last 16 tie effectively decided in the first leg, boss Mauricio Pochettino was able to rest Harry Kane, Christian Eriksen and Mousa Dembele to keep them fresh.
Manchester City would love to pile on the misery for Louis van Gaal when troubled Manchester United visit Eastlands.
Van Gaal saw his United side eliminated from the Europa League by bitter rivals Liverpool in midweek and a defeat in the Manchester derby would be a major blow to their hopes of qualifying for the Champions League.
United are currently four points behind fourth placed City, with fifth placed West Ham also in the hunt as they travel to Chelsea.
Rafael Benitez will take charge of his first home match as Newcastle boss against hated neighbours Sunderland, who have won the last six Tyne-Wear derbies.
Benitez's second bottom side are only one point behind Sunderland in 17th and a first victory over the Black Cats in nine attempts dating back to 2011 would improve thir prospects of avoiding relegation.
Fixtures (1500 GMT unless stated)
Chelsea v West Ham, Crystal Palace v Leicester, Everton v Arsenal (1245 GMT), Swansea v Aston Villa (1730 GMT), Watford v Stoke, West Brom v Norwich
Manchester City v Manchester United (1600 GMT), Newcastle v Sunderland (1330 GMT), Southampton v Liverpool (1330 GMT), Tottenham v Bournemouth (1600 GMT)