"I told the Israeli leadership, don't talk about the Shalit issue and it will gradually be resolved. The more you consider the Shalit issue important, the more they [Hamas] will harden their position," he said.
Shalit was seized by Palestinian fighters during a cross-border raid in June 2006. He is believed to be held somewhere inside the Gaza Strip, which has been run by Hamas since the group seized power in the Palestinian enclave two years ago.
'In good health'
Mubarak's interview follows remarks he made at a joint news conference in Cairo with Shimon Peres, his Israeli counterpart, on Tuesday.
Mubarak said then that Shalit was in good health despite his long ordeal.
He also gave warning that the Middle East peace process could not handle another failure, referring to the 2003 internationally drafted roadmap and a 2002 Arab peace plan offering normalisation in exchange for Israel returning occupied Arab land.
He called on Benyamin Netanyahu, the Israeli prime minister, to "believe that peace and only peace can open a new page in the history of the Middle East."
While Netanyahu has vowed in the past to make Shalit's release a "personal responsibility", Mubarak urged Israel to make "difficult decisions" in the meantime.
Arab and Israeli media reported last month that Shalit was to be imminently transferred to Egyptian safekeeping, pending Israel's release of Palestinian prisoners in exchange.
But Mubarak told Yediot Aharonot that the deal fell apart when Israel insisted on linking Shalit with the reopening of Gaza borders just as the prisoner exchange was about to take place.
"We were on the verge of receiving Shalit from Hamas and of putting him with us until you released some Palestinian [prisoners]," he said.
"You kept saying we'll release this one but not that one and the matter was complicated when you introduced new elements."
Israeli officials visited Egypt twice this month to discuss Shalit's release.