The news follows a setback for Qureia, after the Palestinian parliament on Thursday put off a vote on his new Cabinet because of intense last-minute wrangling.
The Palestinian Authority denied the report, saying Qureia and Arafat only had a "heated dispute."
The vote was rescheduled for Saturday.
Meanwhile, a suicide bomber Thursday detonated explosives near an army base in the West Bank. The attacker was killed, and two Israeli soldiers wounded, one seriously. There was no immediate claim of responsibility.
Also Thursday, CBS News Correspondent Robert Berger reports there are fresh indications that Arafat's health could be deteriorating. A joint team of Jordanian and Egyptian doctors arrived in the West Bank town of Ramallah, to treat the ailing leader, who has been suffering from a mysterious stomach ailment for 10 days.
Palestinian officials say the 74-year-old Arafat has had a high fever, severe diarrhea and vomiting, but they denied a British newspaper report that he suffered a mild heart attack. One Palestinian Web site reported that Arafat might have been poisoned.
"Qureia told Arafat he will not form the cabinet and doesn't want to be prime minister any more," a Palestinian official said.
The officials said Arafat wanted to dismiss Interior Minister Nasser Youssef, who would have security powers, and that Qureia opposed the move.
Israel's Haaretz newspaper reported the cabinet-vote postponement was the result of a dispute over whether the eight ministers sworn in Tuesday by Arafat should have emergency powers or be the permanent cabinet.
Legislator Hanan Ashrawi said that some lawmakers wanted it to remain an emergency cabinet, which would have expired in one month, while others favored confirming the cabinet with a vote in the parliament, which would turn it into a regular cabinet.
Many of the legislators, including those who had not been included in the ministerial line-up, voiced objections to its small size.
"This is a constitutional crisis," Ashrawi said.
Qureia's predecessor as prime minister, Mahmoud Abbas, only lasted four months in office before bowing out with similar problems.
Legislators had already convened in the West Bank town of Ramallah and had been waiting for an hour for the session to begin when the announcement of the postponement was made.
"Everyone has his own script and so we feel that we need more time. We are sorry for troubling you," Deputy Parliament Speaker Ibrahim Abu Najar told legislators.
Israel has had low expectations for Qureia, reports Berger.
Israeli foreign minister Silvan Shalom says Israel won't deal with any regime that's a rubber stamp for Arafat.
"Because he's trying to undermine any regime and any efforts and any prime minister that will move toward peace with Israel," Shalom said.