The incident occurred in the Abu Dis area, near Jerusalem but located in the West Bank. No police officers were hurt, Israeli police said.
There was no indication that the alleged stabbing attempt was linked to Trump's visit. Several such incidents have occurred in recent months.
Further details on the identity and age of the Palestinian were not immediately available.
A wave of unrest that broke out in October 2015 has claimed the lives of 266 Palestinians, 41 Israelis, two Americans, two Jordanians, an Eritrean, a Sudanese and a Briton, according to an AFP count.
Others were shot dead during protests or clashes, while some were killed in Israeli air strikes on the Gaza Strip.
The violence has subsided in recent months.