Locatelli is currently with Italy at Euro 2020, helping the Azzurri reach the quarter-finals where they will face Belgium on Friday.
The 23-year-old came through the youth ranks at AC Milan before joining Sassuolo, initially on loan ahead of a permanent move.
Sassuolo sporting director Giovanni Carnevali confirmed the Gunners were frontrunners to complete a summer move for Locatelli, who has also been attracting interest in Serie A.
“Juventus are the only Italian club we talked to about Locatelli. We met last week with (Juventus sporting director Federico) Cherubini,” Carnevali said to Sky Italia.
“There is interest from their side, we haven’t explored all the terms and evaluations, but we have an excellent relationship with Juventus, so we will continue these talks.”
Carnevali added: “It’s true that other clubs from abroad are interested, Arsenal are one of these and they are ahead of everyone else because they have made us an important proposal.
“Indeed up to now they are the only club which has presented a concrete offer.”
Arsenal boss Mikel Arteta is looking to rebuild the squad following last season’s eighth place in the Premier League, which saw them miss out on European football.
A reported £40million offer for Brighton defender Ben White has been turned down.
The Gunners have also been linked with Benfica left-back Nuno Tavares and Anderlecht’s Sambi Lokonga.