The R's are eyeing Giroud, who scored 12 goals for Montpellier last season.
"I'm in Montpellier to continue my development, to do even better in Ligue 1. But in my mind I hope one day to play in England, it is not a mystery," said Giroud.
"The Premier League is a league that attracts me a lot. Now, however, it is premature to talk about it. "