Cardinal Pell is being questioned by an Australian Royal Commission over what he knew about sex abuse by priests in Australia.
He is testifying via videolink, after he was excused from returning home due to ill health.
He has said he would be happy to meet with the survivors.
In a statement Cardinal Pell proposed meeting small groups of survivors without lawyers or media present on Thursday.
He also said he would be “happy to assist with requests to meet Pope Francis”, but warned he had to “rely on the officials responsible for considering these requests”.
Representatives for the survivors, who earlier said they had lost interest in talks with the cardinal, said they would be prepared to meet him on condition that it was “a level playing field”.
But they said a meeting with Pope Francis was more important to them.
“George Pell has made it very clear he does not have the ability, the power or the interest… so we need to speak to the boss,” abuse victim David Ridsdale said.
Cardinal Pell was questioned over his knowledge of the priest Peter Searson on day three of his testimony on Tuesday.
Searson died in 2009 without facing charges, despite a litany of complaints against him ranging from sexual abuse of children to animal cruelty.
One complaint was that Searson, of the outer-Melbourne parish of Dovetown, stabbed a bird to death with a screwdriver in front of children.
Cardinal Pell told the inquiry he was not adequately briefed by the Catholic Education Office, who told him about the allegations against Searson in a “non-specific way”.
Other senior church members were told of the specific allegations. Cardinal Pell said information may have been hidden from him because of his tendency to ask “inconvenient questions”. (Courtesy BBC)