"If a governor declines, he'll go to the mayors in the state and ask them to lead", the campaign adviser told the broadcaster on Sunday.
More than 30 US states currently have a mandatory mask mandate in force that requires individuals to wear facial coverings while in public. The Centres for Disease Control and Prevention recommends the wearing of masks in public, especially when maintaining social distance is not possible.
During the election campaign, Biden pledged to tackle the ongoing pandemic from a science-based approach, and a new task force is currently being established to coordinate the US response following his potential inauguration.
Since the start of the pandemic, more than 9.9 million cases of COVID-19 have been registered in the United States, resulting in the deaths of at least 237,500 people, according to the Johns Hopkins University Coronavirus Resource Centre.
A recent surge has seen the number of new positive tests reported daily exceed 100,000 since Wednesday.