The Gunners have moved for the 28-year-old after missing out on Mykhailo Mudryk to Chelsea.
Arsenal manager Mikel Arteta still wants to bring in a wide forward to boost their title bid and Trossard has emerged as a top target.
Trossard, who has also attracted interest from Tottenham, wants to leave Brighton and feels he has been “humiliated” by their manager Roberto De Zerbi, according his agent.
De Zerbi said the Belgium international was left out of the Brighton squad for their 3-0 win over Liverpool on Saturday because of his attitude, and he is in the final six months out of his contract at the Amex Stadium.
Arsenal missed out on Mudryk after Chelsea hijacked their move for the Ukraine international, who moved to Stamford Bridge in an £88.5million deal.
Trossard has been in fine form for Brighton this season and has scored seven Premier League goals, including a hat-trick against Liverpool at Anfield.
His last appearance for Brighton came against Arsenal in the latter’s 4-2 win at the Amex Stadium on New Year’s Eve.