The 74-year-old recently confirmed he has no intention of retiring despite resigning the Ireland job after failing to qualify for the World Cup.
According to TMW and Sky Sport Italia, Trapattoni is in exploratory talks with the Paraguayan Federation.
Their current coach is Victor Genes, although he is largely in a caretaker role following Gerardo Pelusso’s exit.
It is reported Trapattoni would be joined by Carlos Gamarra as an assistant manager.
Paraguay finished bottom of the South American qualification group for this year's World Cup with just 12 points from 16 games.
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