Member of the Fatah Revolutionary Council Hatem Abdel-Qader said al-Barghouti is "intending to run for the Palestinian Authority presidential elections", he told Anadolu Agency on Wednesday.
Abdel-Qader told Anadolu Agency that the nomination of al-Barghouti is normal and a "healthy phenomenon" for the electoral race.
"We are with the legitimacy, but when going to the ballots, it is the right of the Palestinian people to give their opinion and elect whom they found suitable."
Al-Barghouthi was detained in 2002 by the Israeli forces and is currently serving a life-term sentence over charges of "directing armed groups that killed and injured Israelis during the Second Palestinian Uprising (intifada)".
Abdel-Qader said he "supports Al-Barghouti to run on behalf of the Fatah group if he is approved by the group in a democratic way."
However, he added that it "would be difficult to get a person in such conditions approved by the Fatah group," referring to him as languishing behind bars for decades.
Two other sources who are close to al-Barghouti confirmed to Anadolu Agency on condition that he intends to run for the presidential elections.
They, however, said a final decision is yet to be taken in the coming weeks.
The Fatah group has yet to comment on al-Barghouti's intention to run for the presidency as it already announced that President Mahmoud Abbas is the group's candidate for the elections.
Meanwhile, a Palestinian NGO, the Palestinian Center for Policy and Survey Research, released results of an opinion poll on Wednesday that the Palestinians prefer al-Barghouti over Abbas to become the president.
Palestinians are set to hold parliamentary, presidential, and National Council elections under a decree signed earlier this month by President Abbas.
The parliamentary elections will be held on May 22, presidential elections on July 31, and the National Council elections on Aug. 31.