The Gunners managed to alleivate some of the growing pressure on the French head coach with a 2-0 win over AC Milan in the Europa League on Thursday night.
Goals from Henrikh Mkhitaryan and Aaron Ramsey secured a commanding first-leg win in the last-16 clash at San Siro ahead of the return leg at The Emirates next week.
Arsenal have lost four of their last five games in the Premier League to fall a long way behind north London rivals Tottenham Hotspur, who are in fourth spot.
The Gunners boss has less than 16 months to run on his current deal to raise questions about his long-term future.
Former Barcelona boss Luis Enrique and Celtic manager Brendan Rodgers have both been linked with a potential appointment at The Emirates.
Ex-Arsenal midfielder Parlour believes Wenger will not be in charge of the north London club at the start of the 2018-19 season.
“I think it is going to be very tough for him to win the Europa League,” Parlour told Sky Sports. “I am going to say no.”
Arsenal finished in fifth place in the Premier League table last term to miss out on a spot in the Champions League for the first time under Wenger.
The Gunners lost 4-2 to Nottingham Forest in the FA Cup third round before a 3-0 defeat by Manchester City in the League Cup final.
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