Diawara currently plays for French non-league side GC Consolat Marseille, and is 24-years-old.
L'Equipe report that Diawara scored 10 goals last season, and has just one year of his current contract remaining.
The striker is the brother of former Charlton Athletic centre-back Souleymane Diawara, who played for the Addicks in 2006/07.
French website Foot National reported earlier in July that Diawara, who was his club's top scorer last season, was interesting Romanian club Steaua Bucharest.
Diawara could be an interesting wildcard addition for Rovers, but he is unproven at Championship level, and not the sort of player the club should be eyeing to replace Jordan Rhodes, should they take the controversial decision to cash in.
Rhodes is claimed by The Mail to be a transfer target of Middlesbrough and Sheffield Wednesday.
Rovers clinched a ninth placed finish in the Championship last season, but are yet to push on in the transfer market this summer.