Ante Budimir, on loan from German side St Pauli at Crotone, has scored in each of his side's last five games, including a goal in the Coppa Italia defeat to AC Milan at San Siro.
And his goal scoring exploits have attracted interest from the Gunners, with scout Tony Banfield running the rule over the 24-year-old during a 2-2 draw against Latina in which the striker found the back of the net.
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Asked by Goal about interest from the Gunners, Budimir responded: "An Arsenal scout was watching me? Really? I didn't know!"
Budimir has enjoyed a change of fortunes in Italy so far this season, scoring nine goals in 19 games in Serie B with Crotone sitting top of the table.
Giroud, meanwhile, has scored 15 times in all competitions so far this season, but with Danny Welbeck still out due to a long-term injury, the Frenchman is Arsene Wenger's only available recognised striker.