The 25-year-old French international has been in scintillating form in Ligue 1 this season, netting 16 goals to put him top of the country's scoring charts.
Rated at around £13million, Giroud has long been on the Gunners' radar, as Arsene Wenger continues his search for attacking reinforcements to ease the goalscoring burden on club captain Robin van Persie.
Arsenal scout Gilles Grimandi has been keeping tabs on Giroud's progress in his native France, and after recently confirming the club's interest in the player, Montpellier acted by raising the forward's minimum fee release clause, from €10million to €16million.
When asked about the possibility of making a summer move to the Emirates Stadium, Giroud said: "I like the Frenchy feel at Arsenal."
Arsenal are not the only Premier League club to have shown an interest in the striker, with Newcastle also believed to be monitoring the situation, whilst Champions League outfits Bayern Munich and Napoli are also poised to make rival bids.