Johnson proposed the idea to the league's commissioner on social media.
The 10-part limited series chronicles the historic NBA team's rise to prominence.
The 37-year-old entrepreneur has reportedly earned more than $385 million in salary and over $900 million in endorsements and investments.
The Golden State Warriors are heading to the 2022 NBA Finals.
Johnson's comments come after chiding Westbrook for his lack of "ownership" and "accountability."
"You don't get vaccinated just for yourself," said Barkley. "You get vaccinated for your family first, you get vaccinated for your teammates second."
“This will allow them to keep their employees and keep their doors open.”
The campaign is raising millions for COVID-19 relief.