"We are at the very beginning stages of even discussing this subject," White House spokesman Sean Spicer said in a statement, Reuters reported.
Aides said no announcement of an embassy move was imminent.
Washington's embassy is in Tel Aviv, as are most foreign diplomatic posts. Israel calls Jerusalem its eternal capital, but Palestinians also lay claim to the city as part of an eventual Palestinian state. Both sides cite biblical, historical and political claims.
Read alsoTrump on protests against him: I recognize rights to express viewsTrump, who vowed during the 2016 presidential campaign to move the embassy, was due to speak by phone on Sunday with Israeli Prime Minister Benjamin Netanyahu, their first call since the U.S. businessman-turned-politician took office on Friday.
Any decision to break with the status quo is likely to prompt protests from U.S. allies in the Middle East such as Saudi Arabia, Jordan and Egypt. Washington relies on those countries for help in fighting the Islamic State militant group, which the new U.S. president has said is a priority.
The U.S. Congress passed a law in 1995 describing Jerusalem as capital of Israel and saying it should not be divided, but successive Republican and Democratic presidents have used their foreign policy powers to maintain the U.S. Embassy in Tel Aviv and to back negotiations between Israel and the Palestinians on the status of Jerusalem.
In early December, then-President Barack Obama renewed the presidential waiver until the beginning of June. It is unclear whether Trump would be able to legally override that waiver and go ahead with relocation of the embassy.
Read alsoCNN: U.S. abstains as UN demands end to Israeli settlementsU.S. diplomats say that, despite the U.S. legislation, Washington's foreign policy is in practice broadly aligned with that of the United Nations and other major powers, which do not view Jerusalem as Israel's capital and do not recognize Israel's annexation of Arab East Jerusalem after its capture in the 1967 Middle East war.
Israel approved building permits on Sunday for hundreds of homes in three East Jerusalem settlements in expectation that Trump will row back on the previous administration's criticism of such projects.