The president-elect said Friedman would "maintain the special relationship" between the U.S. and Israel.
But the announcement sparked anger from liberal Jewish groups. Jeremy Ben-Ami, the president of J Street, called nominating Friedman "reckless," citing his support for settlements and his questioning of a two-state solution with the Palestinians.
The statement doesn't detail how Friedman could work in Jerusalem. However, Trump advisers have insisted in recent days that the president-elect will follow through on his call for moving the embassy.
"He has made that promise," Trump adviser Kellyanne Conway told reporters Thursday. "I can guarantee you, just generally, he's a man who is going to accomplish many things very quickly."
One option Trump allies have discussed would involve Friedman, if confirmed by the Senate, working out of an existing U.S. consulate in Jerusalem. According to a person who has discussed the plan with Trump advisers, the administration would essentially deem the facility the American embassy by virtue of the ambassador working there.
It's unclear how far those discussions have gotten or whether Trump himself has been briefed on the proposal. Trump's transition team did not respond to questions about the matter.
Both Bill Clinton and George W. Bush promised to move the U.S. embassy to Jerusalem, but backed away from the idea once in office.
Israel captured east Jerusalem in the 1967 Mideast war and annexed it in a move that is not internationally recognized. It claims the entire city as its capital. The Palestinians seek east Jerusalem, home to key Jewish, Muslim and Christian holy sites, as the capital of their future state.
Virtually all embassies to Israel are located in or around Tel Aviv.
Jerusalem Mayor Nir Barkat told The Associated Press this week that he has been in touch with Trump's staff about the embassy issue. Barkat said his conversations have led him to believe that Trump is serious about making the move.
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Correction: The original version of this article included an image of a different man with the name David Friedman. We regret the error.