The test, developed by Yale University, is being funded and used on NBA players and staff during the league's restart in Florida. Yale described the test in a press release as "simpler, less expensive, and less invasive" than the common coronavirus testing method that involves a nasal swab.
In addition to not needing a nasal swab, Yale's saliva test has numerous characteristics that should allow it to help improve testing for the virus in the U.S., said Gottlieb, who led the FDA in the Trump administration from May 2017 to April 2019.
"It's also been cross-validated on just about every popular platform for doing testing," Gottlieb said. "So it's easy to use. It's unlikely to be in limited because of shortages in the testing supply chain." He added, "It's something that we can roll out on a very wide fashion."
Yale said it is partnering with a research institute that is also based in Connecticut, Jackson Laboratory for Genomic Medicine, on developing a strategy to implement its saliva test "for a broader audience."
The U.S. has faced various challenges in testing for the coronavirus throughout the pandemic, including supply chain shortages and long delays in returning results. Gottlieb has been critical of the lack of a national testing strategy to direct resources to hot-spot communities.
Beyond Yale's saliva test, Gottlieb said he anticipates other additional variants of coronavirus tests to be available in the U.S. "within the next month."
Specifically, Gottlieb said that lateral flow tests, which provide a readout on a device like a pregnancy test, could be coming onto the U.S. market soon. He said they are popular in other countries and, because they can deliver results in 10 to 15 minutes, could be used to test for the coronavirus in schools and offices. "You put a sample" on a piece of paper, and then you drop some liquid on paper, he said.
"What you're going to see is a lot of this innovation come on the market all at once. This has been worked on for months, and it takes time to move this through the development process," Gottlieb said.
"But I think we're coming at the point right now that you're going to see a real explosion in testing opportunities and you're not going to be so dependent on lab-based testing, which what has been in short supply," he added.
Disclosure: Scott Gottlieb is a CNBC contributor and a member of the boards of Pfizer, genetic-testing start-up Tempus and biotech company Illumina.