The 28-year-old has emerged as a firm January target for the table-topping Gunners, who missed out on a deal for Mykhailo Mudryk over the weekend.
The PA news agency understands talks between Arsenal and Brighton are ongoing.
Arsenal are keen to add strength in depth to their attacking options ahead of the title run-in, with summer signing Gabriel Jesus still some time off returning from a knee injury suffered at the World Cup.
They were close to agreeing a move for Mudryk, only to be gazumped by Chelsea after a delegation from the Blues travelled to Turkey to strike a deal with Shakhtar Donetsk which instead took the winger to Stamford Bridge.
While Chelsea paid a reported up-front fee in excess of £60million for Mudryk, Trossard is likely to cost much less than that.
Trossard, who featured in all three Belgium fixtures in Qatar, was not part of the Brighton squad that beat Liverpool 3-0 on Saturday.
Seagulls boss Roberto De Zerbi openly questioned the forward's attitude as links to Tottenham began to emerge.
But it is Spurs' north London rivals who have now opened negotiations with Brighton, who have a recent history in earning a premium for their key stars.