Martinez has impressed Wenger and the rest of the Gunners' hierarchy with the style of play he demands – a cultured passing game – and by the way the 40-year-old handles himself.
[...] It is believed discussions have already been held within the club about the suitability of Martinez as an eventual replacement.
Speculation toward Martinez taking over will be fuelled by rumours suggesting Wenger is being lined up to replace Gerardo Martino at Barcelona, per Stephen Darwin of Goal.com.
The Arsenal boss dampened such reports by committing his future to his current employers, per Miguel Delaney of ESPN:
Wenger on Catalan suggestions he's on Barcelona shortlist: "My commitment is here and nowhere else", but no developments on new contract.— Miguel Delaney (@MiguelDelaney) March 14, 2014
Wenger is expected to ink a new contract with Arsenal, but this may have hit a hitch, as reported by Neil Moxley of The Sunday People (h/t the Mirror):
The Gunners boss is anxious to retain full control on comings and goings as he prepares to commit his future to the north Londoners.
But there have been repeated delays and Sunday People Sport understands that this is because the long-serving Wenger wants to remain chief hirer and firer.
Should Roberto Martinez be the next Arsenal manager?
While such an issue is unlikely to stop Wenger from penning a new agreement, it promotes thoughts of the 64-year-old's potential departure. As we've seen with Manchester United this season, the changing of an immovable guard can leave the club in turmoil.
David Moyes is yet to exit the colossal shadow left by Sir Alex Ferguson, while Martinez—his replacement at Everton—has significantly progressed the club during his first season.
Martinez's emphasis on thoughtful, passing football has added an extra flow to the Toffees' game. The Spaniard has maintained the club's tough, gutsy personality and implemented extra penetration with the loan signing of Romelu Lukaku and decision to promote Ross Barkley into a first-team role.
Currently on equal points with United in the Premier League, Everton have a game in hand to once again push ahead of the Red Devils.
At 40 years old, Martinez is young enough to be installed with the foreseeable future in mind. Wenger has enjoyed 17 seasons with Arsenal, a club that promotes loyalty throughout its players and staff, suggesting someone of Martinez's ambition could receive similar treatment.
Martinez has won the League One title and FA Cup since Wenger last captured silverware. He boasts a winning mentality and always looks to emerge with a positive result—for better or for worse—as indicated with Wigan's relegation during his last season in charge.
This sense of confidence would be well-matched at Arsenal. Martinez has already shown what he can achieve with a minimal budget at Goodison Park, suggesting he could build an extremely fashionable team if he was able to mobilise Arsenal's funds.
While hypothetical for the moment, Martinez's potential installation as Gunners boss would be a positive step for Arsenal's long-term prospects.