In a series of articles published in September, the daily "Zhamanak" claimed that Kocharian was involved in lucrative imports of pharmaceuticals and owns a chain of drugstores through his wife, Bella.
Citing an unnamed source, it also alleged that Kocharian's eldest son, Sedrak, had purchased a diamond mine in India.
The former president's spokesman and legal counsel said Kocharian and his family members dismissed the reports as libelous. They sued the paper for defamation of character, demanding 6 million drams ($16,700) in compensatory damages.
A "Zhamanak" lawyer, Nikolay Baghdasarian, told a Yerevan court on February 25 that the paper was ready to run a retraction prepared by the plaintiff.
"If they present a reasonable text that doesn't violate the rights of third parties, we will be ready to print it," Baghdasarian said.
The court gave the Kocharian family 12 days to consider the settlement offer.
A spokesman for the ex-president, Victor Soghomonian, told RFE/RL that the family had not yet made a decision on the offer.
The newspaper has already published retractions, sent by the Kocharian family in October, along with its own "explanatory" comments attached to them. It says the family was angered by the background notes.
Baghdasarian said he therefore thought the Kocharian family was unlikely to settle the suit. "We just want to prove that they don't want to refute anything and are pursuing other goals," he told RFE/RL.
Arman Babajanian, the "Zhamanak" editor who was jailed for draft evasion during Kocharian's rule and spent more than three years in prison, earlier denounced the legal action as an "attack on free speech," and that the former president wanted to bankrupt his publication with such lawsuits.
Kocharian was president from 1998 to 2008.