Sharp losses continued Monday, with gold shedding 4.3 percent to $4,682 an ounce and silver sliding almost five percent to $81 an ounce.
That left both precious metals far below respective record highs of above $5,500 and $120 reached last week.
Trump has said that Warsh, a former Morgan Stanley investment banker and Fed governor, "will go down as one of the great Fed Chairmen, maybe the best".
Traders regard Warsh as the toughest inflation fighter among the final candidates, raising expectations that his monetary policy would underpin the greenback.
The choice also eased concerns about the Fed's independence following a series of attacks on incumbent Jerome Powell over his reticence to cut rates as quickly as the president wanted.