Sharon dismissed the Maariv newspaper claim on Thursday, that he had failed to disclose business ties dating to the 1970s with the father-in-law of Elhanan Tannenbaum - who was freed by the Lebanese resistance group on 29 January.
Various politicians have called for the right-wing leader, already under investigation in two corruption scandals, to resign or face an official inquiry.
Opposition parties requested a no-confidence vote in parliament, which is expected on Monday.
Since Tannenbaum's return - in a deal by which Israel also received three dead soldiers in exchange for 400 Arab prisoners - he has been grilled by security agents on allegations he was conducting illicit business when he was abducted in 2000.
Tannenbaum has denied involvement in any criminal activity.
Critics of the German-brokered prisoner swap have said Israel paid too high a price for the former reserve army colonel, and that the deal boosted Hizb Allah's standing in the Arab world.
Maariv reported on Wednesday that Tannenbaum's father-in-law, Shimon Cohen, had been a business partner of Sharon's family in the 1970s and taught him farming methods at their ranch in southern Israel.
Defending himself in front of the parliament, Sharon told reporters he "weighed the considerations based on substance" in deciding on Tannenbaum's inclusion in the prisoner swap.
Israeli Prime Minister Ariel
Sharon denied latest allegations
"I didn't know of the former family ties of Mr Shimon Cohen ... whom I hadn't seen or spoken to in decades."
Ofir Pines-Paz, secretary-general of the main opposition Labour Party, called the Sharon denials "unbelievable".
"The state comptroller is the only one who...can conduct a reliable and serious investigation and I think this is what should happen." said.
Sharon is already facing investigations into two financial scandals - accusations that a businessman friend tried to bribe him and an alleged illegal funding scandal dating back to the 1999 election campaign.
He has denied any wrongdoing. Analysts say he would probably be forced from office if he were indicted.
The confidence votes sought by Labour and other opposition parties in response to the new allegations did not appear to pose any immediate threat to Sharon's grip on power.
His government has easily survived almost weekly no-confidence votes recently despite a rift with far-right coalition partners angered by his plan to uproot Jewish settlements in the Gaza Strip under "disengagement" steps toward the Palestinians.