The midfielder's progress was stalled by a two-year injury absence while at Ipswich, but a string of good displays for Libertad have attracted the Chilean champions' interest
The 25-year-old impressed for the Paraguayans when they took on Universidad in the quarter-finals of this year's Copa Libertadores, although Libertad suffered an agonising penalty shootout exit after drawing 1-1 with the Chilean powerhouse.
According to La Tercera, Civelli will move to Santiago for a fee worth around $1.8 million (€1.5m), forming a major part of the U's renovation efforts for the 2012 Clausura.
Jorge Sampaoli's men have already lost Junior Fernandes to Bayer Leverkusen and Marcelo Diaz to Basel, but have compensated with the acquisitions of Sebastian Ubilla, Enzo Gutierrez and Ezequiel Videla to the squad, which has won the last three Chilean championships.
Civelli, who had also been watched by Sampdoria, started his career at Banfield before moving to Ipswich in 2009, amidst high hopes at Portman Road.
A devastating knee injury kept the midfielder out for almost two years shortly after arriving in England, however, as he only played a total of 17 games for the side before leaving on a free transfer in 2011.