The Gunners have not yet put forward an official bid for the Belgium international but are expected to formalise their pursuit after agreeing on personal terms for a long-term contract.
Arsenal have turned to Trossard after missing out on Ukrainian winger Mykhailo Mudryk, who joined London rivals Chelsea for a deal worth a reported £89 million.
Trossard, 28, has been in recent hot water with Brighton and stated he wants to leave the club after a fallout with manager Roberto De Zerbi.
He was dropped for the Seagulls' 3-0 demolition Liverpool last week, which led to his agent Josy Comhair criticising De Zerbi's treatment of his client.
Trossard joined Brighton from Belgian side Genk in 2018 and established himself as a regular fixture in the side, scoring 25 goals in 116 appearances for the club.
