The London-based newspaper Al-Hayat reported on Saturday that Mubarak would call for a complete halt to Israeli construction in the occupied West Bank and East Jerusalem.
Binyamin Netanyahu, the Israeli prime minister, imposed a settlement freeze on the West Bank last year, but that freeze is set to expire in September. Construction in occupied East Jerusalem, however, continues unabated.
Israeli media reported on Sunday that Netanyahu predicted direct talks would resume by mid-August.
"In recent weeks I have held talks with foreign leaders, which have reached one goal: A more convenient environment for launching direct talks with the Palestinians," Netanyahu said before his weekly cabinet meeting.
Palestinian officials have not yet responded to Netanyahu's remarks, nor have they discussed a timeline for direct talks.
Israel and the PA have been conducting indirect talks since May, mediated by George Mitchell, the US Middle East envoy.
The Israeli and American governments have pushed for the resumption of direct talks, but Abbas wants a guarantee that the Israeli government will completely halt settlement construction.
Direct talks between the two sides were suspended when Israel launched a three-week war in the Gaza Strip in December 2008.