Villa boss Alex McLeish has been scouring the market in search of potential summer transfer targets with AZ Alkmaar's Australian midfielder Brett Holman signing a pre-contract agreement, Newcastle's Danny Guthrie being linked and interest confirmed in Fulham's loan striker Pavel Pogrebnyak.
And, reports over the weekend have now claimed that McLeish has cast his net to the French Ligue 1 with Giroud said to be firmly in his sights.
The France international has already fired 17 goals in 26 appearances for Montpellier this season, while his impressive club form resulted in him being handed a full debut for his country in last month's friendly against Germany, in which he was also on target.
A host of top European clubs, including Bayern Munich and Juventus, have been linked but French newspaper L'Equipe reported that Villa are in the hunt for his signature and could be set to make a bid in the summer.
It is thought that a Villa scout watched the striker in action for Montpellier against Nancy on Saturday, while his team-mate defender Benjamin Stambouli is another player who was also watched at the same time.