Sarri takes charge of his first Premier League game as manager of Chelsea today in Huddersfield.
A little more than 24 hours later, Unai Emery gets under way as head of the Gunners when the defending Manchester City champions head to the Emirates.
And Sky Sports commentator Charlie Nicholas says Sarri should have been an option to replace Arsene Wenger at the club.
"This coach has been floating for a few seasons," he said of Napoli's former man Sarri.
"Everyone has been very interested in seeing what they would finally do.
"I thought Arsenal would also have been in their favor, but I do not know if the negotiations continued."
He added: "He likes the pressure game, Napoli improved greatly when he was there."
"I think that players who can pass a ball, with rhythm, first time, a touch, two touches, and make the thing go at a good pace, he likes that.
"That's what you'll be working on."
Sarri made a debut to the new Chelsea goalkeeper Kepa for the trip to the John Smith Stadium, a few days after his change of £ 71m from Athletic Bilbao.
N & # 39; Golo Kante starts at the center of the field in place of the injured Cesc Fábregas.
Willian also receives the go-ahead to play in attack, with Eden Hazard on the bench.
Chelsea: Arrizabalaga, Azpilicueta, Luiz, Rudiger, Alonso, Barkley, Kante, Jorginho, William, Morata, Pedro.
Subs: Danger, Loftus-Cheek, Knight, Moses, Giroud, Zappacosta, Christensen.