The Frenchman, who is the longest-serving top-flight manager having been in charge since 1996, is under contract at the Emirates until the summer of 2019.
Wenger revolutionised English football and elevated Arsenal to a new level, winning the Premier League three times in six seasons.
However, the 68-year-old’s grip on the hot-seat has never looked more fragile, with disquiet among Gunners supporters growing by the day.
Here, The Boot Room profiles four of the leading contenders to succeed Wenger at Arsenal.
The Italian is the current bookmakers’ favourite to replace Wenger, primarily because he is available after being sacked by Bayern Munich in September last year.
Carlo Ancelotti has an enviable pedigree, having managed a plethora of the biggest clubs in Europe.
As well as the Bundesliga giants, his CV features Real Madrid, Chelsea, AC Milan and Paris St Germain.
With Real he lifted the Champions League in 2014, and at the helm of Milan, PSG and Bayern, he won the domestic league titles.
It is his time at Chelsea that would potentially attract the powers-that-be at Arsenal.
Ancelotti’s spell at Stamford Bridge lasted two years, during which he completed the Double by capturing the Premier League and FA Cup in his maiden season.
The 58-year-old was controversially sacked at the conclusion of the 2010/11 campaign, despite having guided the Blues to the runners-up spot.
Perhaps it was their exit to Manchester United in the quarter-final of the Champions League that persuaded the notoriously trigger-happy owner Roman Abramovich to act.
The former Argentina international has long been linked with a move to England, having turned Atletico Madrid into a genuine force during his seven years at the club.
Diego Simeone helped to break the duopoly in Spain when Atletico pipped Barcelona and Real Madrid to the La Liga crown in 2014.
It was an astonishing achievement that catapulted him to worldwide fame and piqued the interest of Premier League chairmen.
Despite severe financial constraints, Simeone also piloted Atletico to the final of the Champions League twice in three years.
On both occasions they were cruelly denied by city rivals Real, losing in extra-time in 2014 and on penalties in 2016.
Atletico currently sit second in the La Liga table and although unlikely to catch runaway leaders Barcelona, they should finish above Real.
Simeone, 47, is known for an uncompromising style of football.
He is a hard taskmaster whose teams are built solidity at the back, rather than attacking flair.
This is typically un-Arsenal, although defensive stability is a quality they sorely lack.
Since 2006, Joachim Low has been at the helm of the German national team.
Boasting a win percentage of 67 per cent, he has overseen a successful period, culminating in Germany’s historic 2014 World Cup triumph.
After thrashing hosts Brazil 7-1 in the semi-final, Germany edged past Argentina to have their name engraved on the famous trophy for the fourth time.
Many thought Low would call it quits at that point, but he stayed on and will lead them into this year’s World Cup in Russia, hoping to repeat their success from four years ago.
If the 58-year-old does then decide to quit, he is sure to be in demand.
On paper, Low would seem to be an ideal candidate to replace Wenger.
He has vast experience of dealing with top-quality players and his mentally-strong Germany side go about their business with a ruthless efficiency.
The only question mark over his credentials centres on the fact he has been out of club management for more than a decade.
If Arsenal do come calling, though, the lure of working on a day-to-day basis in the Premier League – and linking up with fellow countryman Mesut Ozil – could be too strong to resist.
Like Pep Guardiola before him, Luis Enrique had a spell as manager of Barcelona B before eventually taking the reins of the first team.
In his trophy-laden three-year spell at the Camp Nou, Enrique won two La Liga titles and the Champions League.
He opted not to extend his contract at the Catalan heavyweights and has been out of work since it expired last summer.
Enrique is one of the most coveted managers in world football and after a year’s sabbatical, he is certain to have plenty of suitors.
Recently, the 47-year-old has been linked with Chelsea as a replacement for Antonio Conte, whose fractious relationship with the club’s board has sparked rumours he could depart Stamford Bridge.
However, in pure footballing terms, Enrique would fit in perfectly at Arsenal.
His Barcelona side were a joy to behold, particularly in his debut season as they sealed the treble.
The Gunners are synonymous with attractive football and Enrique would adhere to that principle.
However, with potentially the pick of any European club, the probable absence of Champions League action could discount Arsenal from the reckoning.