"I am literally being confronted with that question about 15 minutes before you called," Trump told Time magazine in an interview published on Thursday.
"That was the question. That was my question of the day. So I'll be making a decision."
In an October 15 Time interview, Trump said the Palestinians do not have a visible leader.
He was responding to a question whether Barghouti could unite Palestinians behind a two-state solution and whether he should be released from prison despite Israel's refusal.
Barghouti, 66, was sentenced in 2004 to five life sentences and 40 years in jail after a court convicted him of orchestrating ambushes and suicide attacks on Israelis during the second Palestinian Intifada, or uprising.
He has denied the charges.
As a leader of the 2000 uprising against Israel, Barghouti has maintained good relations with rival leaders from Hamas and other factions and enjoys great respect and admiration among leaders and grassroots of the Fatah movement in the West Bank and Gaza Strip.
Israel views Barghouti as a terrorist leader.
Some experts say Israel fears Barghouti for another reason: an advocate of a two-state solution even as he backed armed resistance to occupation, Barghouti could be a powerful rallying figure for Palestinians.
Many in Fatah draw a likeness between him and the late Palestinian president Yasser Arafat.
In a 20-point, multi-phase plan, Trump this month orchestrated a ceasefire deal to end the two-year war between Israel and Palestinian militant group Hamas that involved Israel receiving 20 remaining living hostages held in the strip in exchange for the release of 2000 Palestinian prisoners.
Israel has so far also received the remains of 15 of 28 deceased hostages.
Two recently released Palestinian prisoners said that eight Israeli security personnel beat Barghouti unconscious during a prison transfer on September 14.
The prisoners, who were in solitary confinement and did not directly witness the assault, said they had spoken to Barghouti shortly after the attack.
Reuters was unable to independently verify their accounts.
The Israel Prison Service called the assertions "fake" and said it "operates in accordance with the law, while ensuring the safety and health of all inmates".
In August, Israel's ultranationalist National Security Minister Itamar Ben-Gvir shared a video showing him visiting Barghouti in prison and telling him, "You will not win".
Who will govern the Palestinians is a key question.
Palestinian President Mahmoud Abbas, 89, controls parts of the Israeli-occupied West Bank but Hamas runs the Gaza Strip, which has been devastated during the war.
Abbas was elected in 2005 to a four-year term but subsequent elections have been repeatedly postponed.
with AP
