Aljazeera's correspondent in Cairo said the Egyptian president is likely to issue an unprecedented decree appointing a vice president to take charge of the country during his absence.
Mubarak, 76, will leave Egypt on Sunday for the surgery the following day. He had called off several meetings with important visitors this month amid rumours about his health.
He put off a meeting with Israeli Foreign Minister Silvan Shalom because of a sprained ankle, an official source said at the time, and a meeting with Palestinian Prime Minister Ahmad Quraya last week also took place later than expected.
But state television showed the president in apparently good health on Wednesday, standing and talking to reporters about Egyptian plans to help the Palestinians with security.
Our correspondent also said that Egypt is putting off the visit of its security experts to occupied Gaza until it obtains guarantees from the Palestinian side that it would accept Egypt's training of Palestinian security forces.
"It was expected that Major General Umar Sulaiman, Egyptian chief of intelligence, would visit Palestine some time in June," high-ranking sources in Cairo told the correspondent.
A meeting is also scheduled in Cairo in July among the various Palestinian groups to prepare for the proposed pull out of Israel from Gaza.