The 25-year-old scored 21 goals last season to help Montpellier win the Ligue 1 title, finishing the season as joint-top scorer in the division. As such, he has sparked the interest of several top clubs.
But Montpellier manager Rene Girard insists it is Gunners manager Arsene Wenger who is leading the chase, and told French radio station RMC: "Arsenal are very interested and Giroud wants to play in England.
"If Arsene agrees with the president, he will sign for them."
Giroud is to consider his future after Euro 2012 with Arsenal favourites to make their second signing of the summer following the acquisition of Germany marksman Lukas Podolski.