Swiss scientists told an al-Jazeera TV documentary the radioactive material polonium-210 was on belongings given to his widow after he died in 2004.
She objected to a post-mortem at the time, but now wants his body exhumed to enable further tests to be carried out.
Arafat's medical records say he had a stroke resulting from a blood disorder.
Mr Arafat's former aide, Nabil Abu Rdeinah, who is now spokesman for Palestinian President Mahmoud Abbas, said "there is no religious or political reason that prevents further investigation into this matter, including exhuming his body" provided the request came from the former Palestinian leader's family.
Another senior Palestinian official, Saeb Erekat, said what was most important was to "secure an international investigation committee through the (UN) Security Council or the International Court of Justice to deal with the matter as a whole".
Many Palestinians continue to believe Arafat was poisoned by Israel, which saw Arafat as an obstacle to peace and had put him under house arrest. Israel has denied any involvement.
Others allege that he had Aids.
Arafat, who led the Palestine Liberation Organisation (PLO) for 35 years and became the first president of the Palestinian Authority (PA) in 1996, fell violently ill in October 2004 at his besieged West Bank compound.
Two weeks later he was flown to a French military hospital in Paris, where he died on 11 November 2004 at the age of 75.
French doctors bound by privacy rules did not release information about Arafat's condition.