"Barghouti is on the list of 70 prisoners Israeli has agreed to release," the source said.
Meanwhile, the al-Bayan newspaper published in the United Arab Emirates reported Tuesday that the same Egyptian source had said that "Israel's consent to release Barghouti or Saadat, or both, will not change Hamas' stance.
"Hamas will not go back on its demand to release 450 prisoners, the names of whom have been included in a list transferred to Israel through Egypt. The timing and the rest of the issues, apart for the list of names, are considered minor as far as Hamas in concerned.
The paper reported that the Shalit deal will be executed in three stages: In the first stage, Israel will release 150 prisoners out of the 450 included on Hamas' list, and in return Shalit will be transferred to Cairo.
In the second stage, which will take place a week later, Israel will release 300 prisoners in return for Shalit's arrival in Israel.
In the third stage, the Jewish state will release another 550 prisoners, the identity of whom will be determined by Israel, including women, minors and people sentenced to short prison terms. Egypt will vouch for the deal's implementation.
The paper went on to report that Israel has asked to launch a direct dialogue with Hamas in a bid to resolve the issue, but that the Palestinian movement refused.
"They asked to hold direct negotiations with Hamas through Egypt, but the organization refused," the Egyptian source said.
He added that Italy has recently got into the picture in an attempt to mediate between the Shalit family and Hamas officials. The Egyptian source also noted that Italian delegations were in close contact with the Hamas leadership in Gaza and have been visiting the Strip endlessly in a bid to resolve the issue.
GIlad Shalit was kidnapped into the Gaza Strip 758 days ago.