To cover that hypothetical scenario, here is a scouting report on Dzemaili.
Dzemaili 2014 FIFA World Cup Summary
Then-Swiss national team manager (since retired) Ottmar Hitzfeld opted for a midfield pairing comprising of Gokhan Inler and Valon Behrami for the 2014 World Cup.
This meant Dzemaili and Gelson Fernandes were the reserve midfielders.
Behrami sat in midfield enabling Inler to charge forward, with the latter starting in the role Dzemaili hoped to play.
That was why Dzemaili only managed 54 minutes at the World Cup, averaging 18 minutes per game in three substitute appearances.
History will not remember Dzemaili's free-kick against France, instead they will remember his double-miss against Argentina.
Box-to-box running distinguishes Dzemaili from most Serie A standard midfielders.
He times his run and ghosts into opposing penalty boxes unmarked, like scoring when Udinese goalkeeper Zeljko Brkic parried the shot of Napoli centre-forward Gonzalo Higuain.
Inter Milan goalkeeper Samir Handanovic palmed Napoli left attacking midfielder Dries Mertens' shot into the path of Dzemaili.
Cagliari goalkeeper Marco Silvestri inadvertently pushed the shot of Napoli centre-forward Goran Pandev towards Dzemaili, who poached another Michu-like goal.
Dzemaili's free-kick against France and rifling a long-range shot past Sassuolo goalkeeper Gianluca Pegolo shows impressive shooting range.
In addition to being a scorer from midfield, Dzemaili is a viable passing outlet, completing 89.6 percent of his 44.3 passes per game.
Last season, he completed 85 percent or more of his passes in 75 percent of his Serie A appearances, per Squawka.com.
Back in 2007, Dzemaili had to rebound from a serious knee injury, per UEFA.com: "Swiss international midfielder Blerim Dzemaili is expected to be out of action for six months after tearing cruciate ligaments in training at FC Zurich."
It debilitated his ability to perform at Bolton Wanderers—he was slated to move to the Trotters when he suffered his injury at Zurich—which halted his career at the then-Premier League club.
"First of all I was injured and then I had the long period as a substitute at Bolton Wanderers," Dzemaili said in 2008, per Michael Krobath at the Credit Suisse. "In the game against Holland I realised that I had not forgotten how to play football."
Dzemaili only played 63 percent of Napoli's Serie A campaign last season.
Arsenal manager Arsene Wenger is already carrying midfielders with a history of injury problems: Aaron Ramsey, Abou Diaby, Alex Oxlade-Chamberlain, Jack Wilshere, Mathieu Flamini, Theo Walcott, and Tomas Rosicky.
It would not be wise for Wenger to take on Dzemaili, who has injury baggage.
Not to underplay Dzemaili's six goals and three assists in league play last season, but he profited from a high-powered Napoli attack, which was stacked from the starting XI to the bench.
Dries Mertens, Gonzalo Higuain, Goran Pandev, Jose Callejon, Lorenzo Insigne and Marek Hamsik combined to score 60 goals and registered 33 assists.
While Dzemaili could be Arsenal's Michu, what happens when Premier League defenders start tracking his runs?
Michu went from scoring 18 goals in his debut Premier League season to two last season.
Being an international-standard footballer, playing top-flight Serie A football since 2008 and regularly scoring from midfield suggests Dzemaili can have a Michu-like impact for Arsenal.
Dzemaili can be a viable backup to Ramsey should the Welshman get injured.
Statistics via WhoScored.com