According to the report, which quoted a senior source in Abbas' office, the Palestinian president made the request during his meeting with Prime Minister Ehud Olmert on Sunday.
The source said that Olmert said he would consider the matter, but made it clear to Abbas that the issue would be discussed in the next meetings between the two leaders.
It was also reported that Olmert said Haniyeh must accept a series of conditions set by Israel, such as having Abbas accompany him as he passes through the different parts of the Palestinian Authority.
Israel prevents the movement of Palestinian ministers and parliament members from the Gaza Strip to the West Bank and vice versa, and therefore the Palestinian government meetings and the Legislative Council meetings are held via video conferencing.
Meanwhile, Palestinian Information Minister Dr Mustafa Barghouti said that the Olmert-Abbas meeting did not express the aspirations of the Israeli people, as Israel was not ready to put an end to the occupation.
Palestinian Deputy Prime Minister Azzam Al Ahmed, a senior Fatah member, said that the Abbas-Olmert meetings were not helpful and that he opposed them.