Arafat officially asked Quraya to become premier and form a cabinet on Sunday, said the president's advisor Nabil Abu Rudaina.
But Qurayaa did not say whether he would accept Arafat's offer to replace US-backed Prime Minister Mahmud Abbas, who resigned on Saturday.
Quraya received endorsement from two key bodies, the Palestine Liberation Organisation (PLO) Executive Committee and the central committee of Arafat's Fatah movement. Both met in the occupied West Bank city of Ram Allah late on Sunday.
Among the first to react to the news was European Union foreign policy chief Javier Solana, who welcomed Quraya's expected nomination but warned that his task would be difficult.
"He will be able to do a good job," said Solana in referrence to Quraya, speaking in Amman following talks with Jordanian and Palestinian officials.
Palestinian Foreign Minister Nabil Shaath said Quraya's nomination would pave the way for a new cabinet "very soon".
"The Palestinian internal crisis will be resolved very quickly," he added.
Ahmad, who is close to Arafat, said it was impossible to envisage a situation in which Abbas would return to power.
Abbas himself remained guarded about his intentions.
He told reporters on Sunday that his "resignation is final", but when asked if he would accept an offer to form a new government, Abbas said: "It is premature to say at this stage."
But Saib Uraiqat, an ally of Arafat who was reappointed negotiations minister last week, said he expected Abbas would return to his post.
"I think the likely option is that he will ask prime minister Abbas to form the government again"
"I think the likely option is that he will ask prime minister Abbas to form the government again," he told the BBC.
Uraiqat also said that Arafat had not yet accepted Abbas' resignation because it had not been received in writing.
Quraya and Abbas worked closely in the run-up to the 1993 Oslo Accords and were the chief Palestinian negotiators of the heavily-criticised agreement which led to supposed Palestinian self-rule in parts of the occupied territories.
Born in Abu Dis, a suburb of east Jerusalem, Quraya worked for years in the banking sector before moving on to join Arafat's Fatah movement.
He was elected as an MP for Jerusalem in 1996 during the first elections in the territories and was later chosen to become parliament speaker.
Israeli soldiers wounded
The diplomatic developments came against the background of continuing violence occasioned by the Israeli occupation.
Three Israeli soldiers were wounded on Sunday when an explosive device went off near their jeep close to the border with the Gaza Strip, a military source said.
They were driving near the Kissufim border crossing at the time of the explosion and were taken to hospital where their condition was not giving cause for concern, the source said.