New Seagulls boss Roberto De Zerbi is keen on reuniting with the Italian midfielder, whom he coached at Sassuolo in Serie A.
Locatelli made 99 appearances under De Zerbi, scoring seven goals and contributing 11 assists.
His impressive form shown at Sassuolo saw him move to Juventus in 2021 on an initial two-year loan with an obligation to buy for €35 million (£31.1 million).
However, Brighton look set to rival Arsenal to the signing of the Italian, who is expected to return from a muscular injury this weekend.
The Seagulls have made a remarkable start to the season as they sit fourth in the Premier League table with four wins out of six.
De Zerbi looks keen to reinforce his midfield that already boasts the likes of Moises Caiceido, Pascal Groß and Alexis Mac Allister.
Locatelli has made six appearances this season before incurring muscular fatigue which has seen him miss four fixtures.
Arsenal are long-term admirers of the midfielder and even tried signing him last summer off the back of his impressive UEFA European Championships outing.
A £34.3 million bid was lodged by the Gunners last summer but Locatelli chose to head to Turin, per football.london.
The Italian has two years left on his current contract with Sassuolo.
Newcastle United are also notably keeping tabs on the former AC Milan midfielder.
Locatelli's connection with De Zerbi may pay dividends in Brighton and Arsenal race for midfielder
Locatelli has previously heaped praise on his former manager De Zerbi, claiming him to be one of the best coaches around.
He said (via Forza Italian Football):
“He [De Zerbi] is one of the best coaches around, and with him you learn a lot. My confidence has grown and now I am more sure of my possibilities."
De Zerbi will want to put him own imprint on the Brighton side having succeeded former manager Graham Potter at the Amex Stadium.
The Italian coach has signed a four-year deal with the Seagulls and is tasked with continuing the impressive work Potter accomplished in transforming the club.
De Zerbi's desire for Locatelli sees him potentially having to beat Arsenal to his signing.
The Gunners may be on the lookout for a new midfield signing, having reportedly seen two bids for Aston Villa's Douglas Luiz rejected this past summer.
Mikel Arteta's side may go back in for the Brazilian but Locatelli's potential availability may see them return for the Italian.