The one-page Egyptian-drafted text, which was circulated to the 15-member council on Saturday and seen by Reuters, does not specifically mention the United States or Mr Trump. Diplomats say it has broad support but will likely be vetoed by Washington.
The council could vote early next week, diplomats said. A resolution needs nine votes in favor and no vetoes by the United States, France, Britain, Russia or China to pass.
Mr Trump abruptly reversed decades of U.S. policy this month when he recognised Jerusalem as Israel's capital, generating outrage from Palestinians. Mr Trump also plans to move the U.S. embassy to Jerusalem from Tel Aviv.
After the decision, Arab foreign ministers agreed to seek a U.N. Security Council resolution. While the draft is unlikely to be adopted, it would further isolate Mr Trump over the Jerusalem issue.
The U.S. mission to the United Nations declined to comment on the draft. U.S. Ambassador to the United Nations Nikki Haley has praised Mr Trump's decision as "the just and right thing to do."
The draft U.N. resolution "affirms that any decisions and actions which purport to have altered, the character, status or demographic composition of the Holy City of Jerusalem have no legal effect, are null and void and must be rescinded in compliance with relevant resolutions of the Security Council."
It calls upon all countries to refrain establishing diplomatic missions in Jerusalem.
"No vote or debate will change the clear reality that Jerusalem" is the capital of Israel, Israel's ambassador to the United Nations, Danny Danon, said in a statement.
Palestinians want the capital of an independent Palestinian state to be in the city's eastern sector, which Israel captured in a 1967 war and annexed in a move never recognised internationally.
The draft council resolution "demands that all states comply with Security Council resolutions regarding the Holy City of Jerusalem, and not to recognise any actions or measures contrary to those resolutions."
A U.N. Security Council resolution adopted in December last year "underlines that it will not recognise any changes to the 4 June 1967 lines, including with regard to Jerusalem, other than those agreed by the parties through negotiations."
That resolution was approved with 14 votes in favor and an abstention by former U.S. President Barack Obama's administration.
(Reporting by Michelle Nichols; Editing by Grant McCool and Alistair Bell)