WASHINGTON — Sheldon G. Adelson, one of the most hawkish supporters of Israel among American Jews, has offered to help fund the construction of a new American Embassy in Jerusalem, according to the State Department, which on Friday said it was reviewing whether it could legally accept the donation.

The total price tag to build the new embassy to replace the current one in Tel Aviv is estimated at around $500 million, according to one former State Department official. While private donors have previously paid for renovations to American ambassadors’ overseas residences, Mr. Adelson’s contribution would be likely to far surpass those gifts — and could further strain American diplomacy in the Middle East.

Before the embassy is built, the Trump administration plans to open a temporary one in Jerusalem. On Friday, it said that it was accelerating the projected opening in time to mark the 70th anniversary of the creation of the State of Israel on May 14.

Even some of Mr. Adelson’s allies expressed concern that if the administration accepts his offer for the permanent embassy, it could be seen as a well-heeled financial contributor effectively privatizing — and politicizing — American foreign policy.