To address that hypothetical scenario, here is a scouting report on Onazi.
Grading Onazi vs. France: A
French central midfielder Paul Pogba scoring the opener was not the turning point in Nigeria's 2-0 round-of-16 defeat.
It was French central midfielder Blaise Matuidi assaulting Onazi and getting away with it.
Prior to being taken out of the game by Matuidi's horrendous "challenge," Onazi bossed midfield.
Onazi completed 86 percent of his passes, per Squawka.com, and constantly surged into France's defensive half.
Nigeria's structure broke down once Onazi was off the field.
Then-Nigerian manager Stephen Keshi, who was not offered a contract extension, vented at referee Mark Geiger's officiating.
"I am not happy with the officiating," Keshi said, per Stuart James at The Guardian. "On two occasions, he [Onazi] had a very bad tackle and nothing was done by the referee."
Onazi is stout, plays with energy and has flashed box-to-box potential.
He stormed his way into the Napoli penalty box and chased down his rebound.
Onazi charged through on goal and clipped the ball over Trabzonspor goalkeeper Onur Kivrak.
Throughout last season, Onazi had moments of genius.
Upon receiving Lazio right-back Abdoulay Konko's pass, Onazi flicked the ball first-time to put Lazio left-winger Senad Lulic through on goal.
An Andrea Pirlo-esque bullet-like long pass to Lulic against Fiorentina shows Onazi has deep-lying playmaking potential.
Onazi created three scoring chances or more in a game on four occasions, per Squawka.com.
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In Onazi's last three seasons, he has yet to play the entirety of a Serie A season (38 games), nor has he started 75 percent or more of league games in a campaign.
Arsenal would be betting on Onazi's upside rather than his output as a top-flight footballer.
One concern with Onazi is his frenetic pressing, which has seen him concede cheap fouls such as cynically hacking down Udinese central attacking midfielder Roberto Pereyra.
Onazi is a tough competitor, a quick passer, a box-to-box runner and has a commanding presence in midfield.
Presuming Onazi has not suffered a career-debilitating injury after Matuidi's thuggery, Arsenal should consider signing the Nigerian international.
Onazi could be on an Aaron Ramsey-like trajectory.
Statistics via WhoScored.com