The Olympique Marseille midfielder is off contract in June and ready to leave OM and France.
Villa are keen to snap up Kamara, who was watched personally by manager Steven Gerrard and chief exec Christian Purslow at the Velodrome a fortnight ago.
However, Mundo Deportivo says Atleti are unconcerned, having been in contact with Kamara's camp for much of the season.
Indeed, it's claimed Kamara has verbally committed to Spanish giants.
Unlike Villa, Atletico can offer Kamara Champions League football next season and a LaLiga title challenge.
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