"If I had a chance to write the president's speech, I would have begun by saying, I'm actually asking Jeff Bezos of Amazon to take a leave from Amazon and take over the effort to get test kits manufactured and distributed everywhere in America," Friedman said on "Squawk Box.
Friedman said he would have tapped Gates, whose charitable foundation focuses on improving global health care and reducing poverty, to "oversee all efforts to come up with a rapid cure for this virus."
In a address Wednesday, Trump announced he was suspending travel from most of Europe for 30 days in an attempt to slow the coronavirus pandemic.
Trump also said he will be asking Congress to provide payroll tax relief for Americans and instructing the Small Business Administration to "provide capital and liquidity" for small businesses.
Friedman said he watched the speech hoping to gain confidence in the government's response to the global pandemic.
"I was not reassured, and the market clearly was not reassured," Friedman said.
U.S. stocks sank Thursday morning as investors remained concerned about an economic slowdown due to the coronavirus.