Spot gold edged up 0.1% to $1,905.91 an ounce by 0905 GMT, reversing losses from early Asian trade to climb back above $1,900. U.S. gold futures eased by 0.2% to $1,912.00.
Bullion has gained 2.5% this week, heading for its biggest weekly percentage rise since early August.
"It will now be a wait-and-see game where gold will attract some bids. It's certainly not a market where I see any appetite for selling gold," said Saxo Bank analyst Ole Hansen.
Trump said on Friday that he and his wife Melania, who had also tested positive, were going into quarantine, a day after a top adviser tested positive for the virus.
"It really is a question of how it's going to pan out - is it going to be a (UK Prime Minister) Boris Johnson-type illness or (Brazil President) Jair Bolsonaro one, come and gone without any real impact," Hansen added.
European equities fell and U.S. futures sank on the news, only a month ahead of the Nov. 3 presidential election. [.EU][.N] [MKTS/GLOB]
"Depending on how this situation evolves over the weekend, notably if more members of the U.S. Government senior leadership are diagnosed positive, gold could be set for an extended rally," said Jeffrey Halley, a senior market analyst at OANDA.
"The only cautionary note will be gold's performance if the equity sell-off accelerates today."
Investors often sell bullion to cover losses elsewhere and meet margin calls when there are sharp sell-offs in wider markets.
Gold's latest jump came despite a buoyant dollar
Investors now await a U.S. non-farm payrolls report later on Friday. Payrolls are expected to have risen by 850,000 in September, a Reuters survey shows.
Elsewhere, silver fell 0.3% to $23.82 an ounce, platinum dropped 0.7% to $889.88 and palladium eased by 0.4% to $2,304.98.
By Nakul Iyer
