Netanyahu, now Israel's opposition leader, is demanding 837,000 shekels ($269,000) in damages, in a lawsuit revolving around comments Olmert made in two Israeli media interviews last year that Netanyahu, his wife and elder son are mentally ill.
Those remarks, Netanyahu said in bringing the case, were "ugly, blatant lies" that slandered the family.
At a preliminary hearing attended by both former leaders, Olmert was asked by the judge for the basis of his remark that "what cannot be fixed is the mental illness of the prime minister, his wife and elder son", according to published reports by Israeli journalists at the session in Tel Aviv.
Olmert replied that he had consulted with experts and people close to the Netanyahu family before making the remarks, the reports said.
Proposing a compromise, Judge Amit Yariv suggested that Olmert state that his comments about the family's mental health were only an opinion rather than a fact, a spokesman for Netanyahu said, adding that the Netanyahus agreed to the idea.
There was no immediate indication that Olmert would accept the compromise.
Netanyahu's wife Sara and their son Yair, a vocal right-wing figure on social media, were also at the session.
($1 = 3.1161 shekels)