However, Anigo expects that the temptation of Champions League football will be enough to convince the 25-year-old to stay put.
"This is a player who wants to play in the Champions League next season and it seems we are not going to get there," Anigo told OMTV.
"That is why I do not believe we have any chance to sign him. I don't believe he will leave France this summer because he will want to play with Montpellier in the Champions League."
Giroud has scored 18 goals in the league this season.