The Premier League side are hoping to add a left-sided midfielder in the summer.
According to The Argus, new boss Graham Potter is hoping to sign the Belgian international Trossard.
A Belgian source, HLN Sport, indicated that Brighton had a bid rejected for the prolific wide man.
Genk are holding out for nearly £18million for Trossard.
The attacker managed 22 goals and 11 assists in 47 games for the Belgian side last term.