The Spanish capital club are on the lookout for potential replacements for the Colombian and have identified the in-form Frenchman as a strong candidate to fill the gap
The Colombia international has been tipped to leave Atletico after enjoying an impressive debut season at the Spanish club following his €40 million transfer from Porto last summer.
Atleti have refused to say whether they will be able to fend off interest in the highly-rated striker, and Spanish sources claim that Los Rojiblancos are already planning for life without the 26-year-old.
Giroud, an international for France, has been in sensational form this season, having so far netted 21 Ligue 1 goals as Montpellier sit at the summit, on the verge of claiming the first title of their history.
Should negotiations for Giroud fall through, Atletico will reportedly move for Burak Yilmaz, who topped the Turkish Super League's scoring charts with 34 goals.