After a three-hour meeting with Arafat late on Monday, the legislators said the president was likely to promise Quraya speedy measures to satisfy growing calls for anti-corruption reforms.
"Arafat agreed to speed up the reform drive to end the state of lawlessness in the Palestinian territories," legislator Hanan Ashrawi said.
A power struggle has been brewing in Gaza in anticipation of Israeli Prime Minister Ariel Sharon's plan to withdraw troops and settlers from the occupied territory by the end of 2005.
Arafat's leadership was challenged this month when Palestinian fighters linked to his Fatah faction sparked political chaos in Gaza by kidnapping a number of officials and demanding he should reform the Palestinian Authority and security forces.
Quraya, widely viewed as a moderate voice in the Palestinian Authority, has called for reform and submitted his resignation to Arafat last week because of the issue.
He wants Arafat to relinquish control, both direct and indirect, over security forces. So far, Arafat has agreed to only superficial changes.
Legislator Ashrawi said Arafat would demand the Palestinian attorney general begin legal procedures against any officials involved in corruption. Another legislator said Arafat would give his interior minister powers to fight corruption.
The legislators were part of a 14-member committee formed by the Palestinian parliament last week to convince Arafat to speed up reform and enforce the rule of law.
Quraya is reportedly frustrated at his lack of power to rid public bodies, especially a muddle of security agencies, of feuding and cronyism and make them more democratic and accountable.