The former Italy and Juventus coach is seeking a new challenge after being let go by the Republic of Ireland in September 2013
The Italian coach had previously expressed a desire to manage a team at the 2014 World Cup in Brazil and has been linked with a number of national teams, including Mexico.
However, according to a report in the Irish Independent, the former Juventus and Italy coach has most recently been linked with managerial post with South American outfit Paraguay, who failed to qualify for the tournament after finishing bottom of the CONMEBOL qualification group.
Trapattoni, who was relieved of his duties as Ireland manager in September 2013, had recently been mentioned as a possible candidate for several club positions.
The 74-year-old was this week rebuffed by Bundesliga side Hannover 96, who opted to appoint former Turkey international Tayfun Korkut instead.
Despite rejecting Trapattoni's application, Hannover chief Martin Kind said that it was "an honour" for the Italian to be interested in the role.
"My personal highlight was Trapattoni," Kind told Bild. "It was an honour for us that he was interested in 96."