The BBC reports that Egypt might support the idea of an Israeli pullout from the Gaza strip. It is, however, still "not prepared to take on responsibility for Gaza security."
Israeli Foreign Minister Silvan Shalom has described as "very promising" his talks with Egyptian President Hosni Mubarak in Cairo.
Mr Shalom indicated that a proposed Israeli withdrawal from the Gaza Strip was discussed but gave no details.
Earlier, Mr Mubarak said Egypt was not prepared to take on responsibility for Gaza security after a pull-out.
Mr Shalom's visit is part of a flurry of diplomatic activity prompted by the Israeli proposal.
An US team led by Assistant Secretary of State William Burns is due to hold talks in Israel later on Thursday, while Mr Sharon is expected to have his first meeting next week with Palestinian Prime Minister Ahmed Qurei.
The BBC's Wyre Davies in Jerusalem says Israel's declaration about its proposed withdrawal from Gaza was initially criticised for being one-sided and for failing to involve the Palestinians.
But our correspondent adds that while there are still a number of questions and concerns over the Israeli plan, it is clear that the idea is gathering support and credibility.
In Cairo, Mr Shalom wanted to gauge Egypt's views on the pull-out and establish how it could stop weapons crossing over its border into a Palestinian-run Gaza.
But last week Mr Mubarak dismissed the idea, saying it would be a trip that could bring Egypt into conflict with the Palestinians or even the Israelis in what is likely to be a volatile situation in the territory.
It was the first visit to Egypt by a senior Israeli official in 18 months, the BBC's Heba Saleh in Cairo reports.
Relations between the two countries had deteriorated as Israel and the Palestinians sank into deeper violence, but now - with a prospect of an Israeli pull-out from Gaza - some warmth has crept back into relations, our correspondent says.