The 24-year-old is set to have a medical at the Amex Stadium club this week.
Sky Sports says he will seal a £18 million transfer to the Premier League side.
The Belgian will be the second signing of the summer for new Brighton boss Graham Potter.
Brighton are hoping to build a team that is good enough to climb the Premier League table and play exciting football.
Trossard fits the bill, given his creativity and goal output from wide positions.