The 25-year-old is currently with the France squad at Euro 2012 after playing an integral role in Montpellier's surprise Ligue 1 title success last season.
He is tipped to leave the French champions during the summer and has several clubs on his trail ahead of an anticipated £12million deal.
Borussia Monchengladbach have expressed an interest in signing Giroud, who has previously admitted he would be willing to join fellow Bundesliga side Bayern Munich.
However, Montpellier coach Rene Girard revealed earlier in the week that Arsenal are leading the chase for Giroud and suggested the forward's priority is to move to the Premier League.
Giroud is flattered to be the subject of such interest, but is putting his club future on the back-burner during France's bid to win the European Championship.
"It's nice that people talk about me but I can't talk about my future right now," Giroud is quoted by the Daily Star Sunday.
Arsenal are also in the market for Giroud's France team-mate Yann M'Vila and have already boosted their attacking options for next season by signing Germany international Lukas Podolski.