Hezbollah has said in the past that Arad was believed to be dead.
However, Ehud Olmert, the Israeli prime minister, told his ministers on Sunday: "It has been over 20 years since Ron's disappearance, we have no certain information about what happened to him at all."
Sunday's deal would see Israel release the five Lebanese and the remains of Hezbollah fighters in exchange for the bodies of Ehud Goldwasser and Eldad Regev.
The soldiers were captured by Hezbollah fighters in a deadly cross-border raid on July 12, 2006 that sparked a devastating 34-day war in Lebanon.
After this part of the deal is over, Israel will decide within 30 days which Palestinian prisoners will be released, according to media reports.
The document approved by the cabinet on Sunday states that Israel alone will decide how many Palestinians will be released.
The deal has drawn some criticism in Israel, and Meir Dagan, the Mossad spy agency chief, voiced strong opposition during Sunday's cabinet meeting.
A controversial part of the agreement is the release of Samir Kantar, a Lebanese prisoner and member of the Palestine Liberation Front who is serving a 542-year sentence for killing two men and a four-year-old girl in a 1979 attack in northern Israel.
Mark Regev, Olmert's spokesman, said Israel had "a moral obligation" to bring back its servicemen.
"In these negotiations we have been forced to deal with Hezbollah, a cynical terrorist organisation that has no qualms about manipulating the pain of our servicemen families," he said.
Olmert told the cabinet on Sunday the two soldiers were dead.
"As far as we know, they were killed during the kidnapping or died from their wounds soon after the incident".
Hezbollah hailed the deal as a victory for the Shiite militia.
Hashem Safie Eddin, Hezbollah executive council chief, said: "The world could not achieve the Israeli goal of recovering its soldiers without the resistance dictating its terms: the release of prisoners".