Officials are saying that the federal government has no plans to establish vaccine passports. However, private companies and state government can make the moves if they choose to.
New York City is already implementing a rule where you have to have proof of being vaccinated in order to eat indoors at certain restaurants, work out indoor at gyms, and attend entertainment events indoors.
The city of Los Angeles is also considering requiring residents show proof of vaccination for gyms, restaurants and indoor sporting events. What city is next? I wonder if Chicago will take it there, we'll see.