Scouts from the Swans have watched the Celta Vigo striker but, according to Spanish paper AS, Atletico are drawing up a bid for the 25-year-old.
Aspas has scored six times in La Liga so far this season, form that is thought to have interested Atletico manager Diego Simeone.
Celta have acknowledged that they face a battle to retain Aspas' services, saying: "It will be difficult to keep Iago at the club after the end of the season."
Swansea boss Michael Laudrup has had success raiding the Primera Liga before, having signed Premier League top-scorer Michu in the summer.
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