The U.S. government is negotiating the purchase of an additional 100 million doses of the Pfizer/BioNTech COVID-19 vaccine, but the company may not be able to provide them until the third quarter of next year, according to Pfizer CEO Albert Bourla.

"We can provide them — the additional 100 million doses — but right now, most of that we can provide in the third quarter," Bourla told CNN Chief Medical Correspondent Dr. Sanjay Gupta on "New Day" Monday. "The U.S. government wants them in the second quarter. We are working very collaboratively with them to make sure that we can find ways to produce more or allocate the doses in their second quarter as well, but we haven't signed this agreement yet."

So far, the company has 50 million doses of the vaccine scheduled for distribution this year. They have already been manufactured, Bourla said, with 25 million going to the United States and the other 25 million to the rest of the world. He added that next year, U.S. and European manufacturers will create another 1.3 billion doses while the company maxes out capacity in its plants. 

From those doses, 100 million will go to the United States in the first quarter of the year,  with the other 1.2 billion being sent to other countries. 

Meanwhile, Bourla told CNBC's "Squawk Box" that he hasn’t gotten his company’s shot yet and that he and other executives will not “cut the line." He said he'll be willing to be recorded getting the vaccine if it will help encourage others to get their shots.

He also encouraged Americans to "trust science" and to get vaccinated when it is their turn. 

"This is a vaccine that was developed without cutting corners from a company with 171 years of credentials,” Bourla said. "This is a vaccine that was developed in the spotlight, in the daylight, with all the data being put in a server.”

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