On Monday, lawyers and Common Pleas Judge Teresa Sarmina were scheduled to meet at Bevilacqua's home at the St. Charles Borromeo Seminary, the Philadelphia Inquirer reported.
Bevilacqua was scheduled to be questioned about Monsignor William J. Lynn, Bevilacqua's former aide, who is accused of recommending two priests for assignments that put them in direct contact with children. Prosecutors say those priests went on to sexually assault two boys.
Lawyers for Bevilacqua argued he was unfit to testify as he suffers from dementia. The special hearing comes after the judge found Bevilacqua to be competent to testify.
Prosecutors asked for the proceedings to be held in open court, but Sarmina agreed to Bevilacqua attorney Brian McMonagle's request for a closed hearing in the cardinal's home.
The judge also imposed a gag order, prohibiting lawyers from talking about the case at least until Lynn's trial, which is scheduled to begin in March.
Two other priests also face charges of child sex abuse in the case.