"Certainly, flu and Covid is not going to be a pretty picture," Donigan said on "Squawk Box." "You don't want to get the flu and Covid. Plus, it's going to be confusing to know whether you have the flu or Covid."
For that reason, Donigan, a former health-care executive who joined Rite Aid in 2019, urged Americans to get flu shots this year. She noted that less than 50% of Americans received the flu shot last year.
The Centers for Disease Control and Prevention hopes that figure will increase to about 65% this year, according to its director, Dr. Robert Redfield, who has previously warned of the health challenges the U.S. could face with both the coronavirus and seasonal flu circulating.
Donigan said Rite Aid is "anticipating a significant surge" in the need for flu shots. The Pennsylvania-based drug store chain has started to administer the vaccinations this year, she said, "and we're already seeing a lot of flu activity."
"Luckily, we, among others, are doing both flu tests and Covid tests and so you can find out which is which," she said. "But the best thing to do is not get the flu in the first place."
The flu shot is not 100% effective, Donigan noted. But according to the CDC, it can reduce the likelihood of going to the doctor with flu by 40 to 60%.
In a WebMD interview earlier this month, Redfield said that being vaccinated for the flu can also reduce the severity of illness, should a person still become infected. That is especially important because it can reduce the strain on the health-care system, he said, which has been a priority during the coronavirus pandemic.
"I've seen hospital intensive care units stretch by a severe flu season, and clearly, we've all seen it recently with Covid. So by getting that flu vaccine, you may be able to then negate the necessity to have to take up a hospital bed," Redfield said. "Then that hospital bed can be more available for those that potentially get hospitalized for Covid."
Shares of Rite Aid were slightly higher in premarket trading. The stock, while down about 12% so far in 2020, remains up more than 150% in the past 12 months.