Raffaele Sollecito, who was also acquitted in Kercher's death, has also spent the past four years behind bars. He was invited to visit the Knox family in Seattle by the 24-year-old's father.
Curt Knox said the only time the former couple got to talk was after Tuesday's verdict when they were being whisked away.
Sollecito was dating Knox, a former University of Washington student, in Perugia in fall 2007 when the Kercher was stabbed to death.
According to Sollecito's lawyer, the 27-year-old is resting and still shaken from the experience.
While Sollecito's lawyer said his client would likely take up the offer eventually, it was unclear when that visit might be.
The Associated Press contributed to this report.