You've probably been hearing a lot about how it's more important than ever to get a flu shot this year. Health experts are worried about the collision of flu season and the coronavirus pandemic. Doctors have warned people that they can get COVID and the flu at the same time, with potentially serious complications. But while it's important to take all the precautions you can, the nation's leading infectious disease expert Anthony Fauci, MD, recently said you might want to wait a bit before getting the flu shot.In a Sept. 10 interview with actor Jennifer Garner on Instagram Live, the director of the National Institute of Allergy and Infectious Diseases (NIAID) said that he gets the flu vaccine in mid- to late October, and recommended that others follow suit."You really should get a flu shot," Fauci said. "I wouldn't necessarily get it now, in September, because there is evidence that, in fact, the immunity might wear off when you get to February and early March."Fauci called his advice "unofficial," and it's important to note that there is some debate among doctors around when to get the flu shot. In an interview with the New York Post, Michael Richardson, MD, of One Medical, said, "We always recommend getting the flu shot early—that's in September, October. That's because flu season comes around in October."But as Richardson acknowledged, there is no exact date when flu season starts, and it can last until as late as May. Because it takes two weeks to develop immunity, it makes sense for doctors to recommend patients get the vaccine as soon as possible. On the other hand, Fauci's concern also carries weight, since an early flu shot might mean losing immunity to the virus before flu season is over.RELATED: For more up-to-date information, sign up for our daily newsletter.And Fauci is not the only doctor who recommends holding off on the shot. If you are older of immunocompromised, you might want to consider waiting "a little longer before getting vaccinated," David Hirschwerk, MD, an infectious disease specialist at Northwell Health, told CNBC Make It. For everyone else, however, "you can get the flu shot any time."Meanwhile, if you're worried that they'll run out of the vaccine before you get your flu shot, Fauci told Garner that's an "unlikely" scenario. "Every year there's a certain [amount] of flu shots that we just don't use," he said. And for more advice on staying healthy, these are The 2 Vitamins Dr. Fauci Says You Should Take to Boost Immunity.