Following a hugely impressive 25-goal season capped by the Ligue 1 title, the France international has been linked with a move to several other top clubs including Bayern Munich in recent weeks.
But Montpellier manager Rene Girard has revealed that the north London club are leading the chase and claims a deal could be close.
Girard said, "Arsenal are very interested and Giroud wants to play in England, if Arsene [Wenger] agrees with the president [Louis Nicollin], he will sign for them".
Currently, Giroud is away on international duty with this country in Poland and Ukraine for Euro 2012, and has said that no decision on his future will be made until after the conclusion of the tournament.
Along with the previously confirmed signing of Koln striker Lukas Poldolski, a move for another striker has led to speculation over the possibility of Robin van Persie leaving the Emirates being increased.
The Dutchman held talks with the Arsenal hierarchy before Euro 2012, but with no indication from either camp as to its outcome, in the addition to rumours of interest from Manchester City, the striker’s future still remains uncertain.