The reports surfaced after a senior Palestinian official said "a heated argument" took place between the pair on Saturday following a decision taken by the cabinet to make security and financial reforms.
But Quraya, who met with German Foreign Minister Joschka Fischer in Berlin on Tuesday, told reporters: "Resigning? Why? I am here as the prime minister. I am not thinking about that."
A Palestinian offcial had earlier said that Arafat rejected the cabinet decision and considered it an infringement on his powers.
"But an angry Abu Ala (Quraya) told ministers after his argument with Arafat that he wants to resign and that he's thinking of quitting because he can't go on like this any more."
Arafat has come under intense world pressure, especially from the US, to appoint a prime minister to fight corruption, pursue peacemaking and carry out reforms in the Palestinian Authority.
If Quraya were to resign it could further isolate the veteran leader.
International aid to the Palestinian Authority has been cut in half since 2001 because of its lack of transparency in spending donor money.
But Quraya has been walking a tightrope between maintaining a working relationship with Arafat and improving ties with Washington.
"Resigning? Why? I am here (in Berlin) as the prime minister. I am not thinking about that"
Palestinian prime minister
Palestinian officials said Arafat, besieged in his battered headquarters in the West Bank city of Ram Allah for more than two years, has agreed to make some administrative and financial reforms, but will not hand over control of security.
"Quraya is seriously thinking of carrying out a cabinet reshuffle which could include changing the interior minister and bringing in lawmakers to strengthen his standing in the Legislative Council," one senior official said.
"This could lead to rising tensions with Arafat but it is a necessary step to give Quraya a higher margin to manoeuvre to advance peace and make reforms."
Arafat and Quraya are the Palestinian Liberation Organisation's two most senior leaders.
Quraya's main claim to fame, thus far, is his role in the Oslo Peace Accords with Israel in 1993.
The accords led to limited autonomy for Palestinians in the West Bank and Gaza Strip.
But they failed to lead to the setting up of a viable state, as many Palestinians had hoped.