The text has not been formally circulated to the full 15-nation Security Council, a move that can only be done by a council member, said the diplomats, speaking on condition of anonymity. As a result, it remains unclear when, and if, it will be put to a vote.
It calls for "the full withdrawal of Israel ... from all of the Palestinian territory occupied since 1967, including East Jerusalem, as rapidly as possible and to be fully completed within a specified timeframe, not to exceed November 2016."
The draft, which was obtained by Reuters, is likely to be met with opposition from veto-wielding member the United States, a key ally of Israel.
"We are aware of President Abbas' plan and we continue to believe, to strongly believe, that the only way to a negotiated solution is through negotiations between the two parties," U.S. Ambassador to the United Nations Samantha Power told reporters on Tuesday.
Israel accepts the idea of a "two-state solution" of an independent and democratic Palestinian state living alongside Israel, but has not accepted the 1967 borders as the basis for final negotiations, citing security and other concerns.
Palestinian President Mahmoud Abbas told the UN General Assembly on Friday there was no value in peace talks with Israel unless the goal is ending its 47-year occupation within a "firm timetable."
In the same speech, Abbas also accused Israel of genocide during the 50-day conflict in the Gaza Strip between Israel and Palestinian militant group Hamas, which ended in late August with an Egyptian-brokered ceasefire. Hamas controls Gaza.
Prime Minister Benjamin Netanyahu reacted angrily during his UN address on Monday, describing the allegations as "shameless." He expressed his support for a "historic compromise" with the Palestinians, but offered no new details of what such a compromise would envisage.