The 31-year-old former France international has made 13 appearances for Rovers so far this season and has attracted interest from the Ligue 1 strugglers.
They are looking for defensive reinforcements and are targeting Arsenal's Sebastien Squillaci as a back-up should their bid for Givet fail.
Evian chairman Patrick Trotignon told L'Equipe: "Givet? We are in talks and it is really serious, but the Englishmen are not easy.
"They don't want to let him leave just like that. If Gael would come, it would be on loan.
"Squillaci? We won't be able to sign both of them."
Evian currently sit 17th in Ligue 1, three points above the relegation zone.