The paper said Shimon Peres's visit had nothing to do with a breakthrough in a deal for the release of Gilad Shalit, the Israeli soldier kidnapped in 2006 by Hamas, the Palestinian faction.
After the meeting at the presidential palace, Hosni Mubarak is scheduled to host Peres for lunch together with Egyptian political and military leaders, according to Haaretz.
Peres is expected to return to Israel on Sunday evening.
The visit comes a day after Mubarak was quoted by the Kuwait News Agency as accusing Israel of undermining the peace process.
"You are placing new obstacles in the path to peace through your call to recognise the Jewish character of the state, to negotiate on interim borders for the Palestinian state and ruling out al-Quds from the final status negotiations," Mubarak reportedly said.
He also urged Israel to lift the siege of Gaza and to answer calls for peace "within a specified time frame and [with] clear guarantees".
Egypt, which has been working to mediate reconciliation between Palestinian factions Hamas and Fatah, has not lost hope, Mubarak was quoted as saying.