Trump will undergo televised medical evaluation on Friday night, Fox News announces

He's also written a few books:

False Alarm: The Truth about the Epidemic of Fear (2005, link)
Inside flap:
Life today for citizens of the developed world is far safer, easier, and healthier than for any other people in history. Modern medicine has all but wiped out many diseases that once were common killers. Science and technology have given us countless devices that protect our bodies from injury, secure our property, and warn us of impending disaster. And modern intelligence gathering can pinpoint threats to our domestic security as they arise. So why is an epidemic of fear sweeping America?
The answer, according to nationally renowned health commentator Dr. Marc Siegel, is that we live in an artificially created culture of fear.From the anthrax panic to the SARS "epidemic," from "official" rumors of bioterror to Orange alerts to West Nile virus-- the media continually bombard us with breaking news of yet another super-bug, terrorist plot, or natural disaster that's about to wreak havoc. Most of the time the disasters never materialize. But even if they did, the odds that any of us would suffer harm from them is infinitesimally small-- especially when compared to the much greater risks of dying in a car accident or from coronary heart disease.

Bird Flu: Everything You Need to Know About the Next Pandemic (2006, link)
Editorial review:
The most important thing to know about the avian flu pandemic is that it probably ain't coming, argues this brisk debunking of the latest medical scare story. Siegel, an associate professor at the NYU School of Medicine (False Alarm: The Truth About the Epidemic of Fear), cites evidence that the death rate from avian flu could be much lower than the reported estimate of 50% and it will probably not mutate to be readily transmissible between humans. And unlike the 1918 Spanish flu pandemic, Siegel contends, a new bird flu pandemic would face effective public health measures and medical treatments. Revisiting the West Nile virus, anthrax, SARS and bioterrorism panics, Siegel sees bird flu as the latest "bug du jour" hyped by government and media alarmism. Meanwhile, he complains, attention is diverted from far more deadly diseases like AIDS, malaria and regular flu. In his own lapse into medical panic, he insists that stress induced by medical panics is itself a serious medical problem.

Swine Flu: The New Pandemic (2009, link)
Without minimizing the risk for current strains of H1N1 to become more dangerous, author and physician Siegel (Bird Flu: Everything You Need to Know About the Next Pandemic) offers a calming dose of reality regarding swine flu; while ""we need to be in awe of the potential for damage,"" Siegel prescribes ""learning to understand why the likelihood of the worst case coming to pass is awfully low."" A practicing internist, associate professor and newspaper columnist (as well as a parent), Siegel addresses many common concerns over the H1N1 pandemic, giving clear explanations about the nature of the virus, historical examples, risk factors, available treatments, and more. He also explains how the 1918 flu pandemic killed as many as 50 million people-the chaotic aftermath of WWI played no small part-and how the present pandemic is simply incomparable. Breaking down the science of virus transmission, Siegel explains the conditions by which H1N1 could mutate into something more dangerous, as well as the anti-viral drug, Tamiflu, and the swine flu vaccine (and how the vaccine's safety is being assured).Taking a balanced approach, Siegel offers a realistic and concise guide for any concerned citizen.

What an odd coincidence!

there's no reason to believe [COVID-19 is] actually more problematic or deadly than influenza,"

To be fair, this was basically the consensus opinion up till mid February or so. Here you can see what the media was saying around that time. Highlights:

“Don’t worry about the coronavirus,” BuzzFeed wrote on Jan. 29. Worry about the flu.” On Jan. 31 – the same day the Trump administration imposed a ban incoming visitors from China – the “explainer” news site Vox was telling readers, “Is this going to be a deadly pandemic? No.” On Feb. 1, the Washington Post ran an article headlined, “Get a grippe, America. The flu is a much bigger threat than coronavirus, for now.”
[...]
By Feb. 3, China had extended the quarantine to 50 million people and imposed a travel ban on 16 cities. Now the Washington Post was worried, but about government’s response, not the virus, writing a critical story with the headline “Why we should be wary of an aggressive government response to coronavirus.” The complaint was that harsh measures “scapegoat already marginalized populations”
[...]
On Feb. 7, The Daily Beast was saying, “Coronavirus, with zero American fatalities, is dominating headlines, while the flu is the real threat.” As late as March 4, CNN’s Anderson Cooper was telling viewers, “So if you’re freaked out at all about the coronavirus, you should be more concerned about the flu.”

This is a right leaning news site so it mostly focuses on the "liberal" media but I'm sure there are plenty of conservative sites that said similar. It would be interesting to know his current opinion on HCQ though.