After failing to lead Ireland to the 2014 World Cup finals, Trapattoni insisted he is not yet thinking of retirement.
According to TMW and Sky Sport Italia, Trapattoni is in initial talks with the Paraguayan Federation regarding the position.
Victor Genes is the man currently in charge of the Paraguay national side, but 74-year-old Trapattoni is looking to take over and possibly bring in Carlos Gamarra as his assistant.
The veteran has been linked with a number of side in recent weeks, including Hannover, Lazio and the Mexican national side.
Paraguay have had Italian management previously when Cesare Maldini lead the country to the 2002 World Cup.
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