"With Omicron we need to wait and see because we have very little information. We may need it faster," Bourla told CNBC's "Squawk Box."
"When we see real-world data, will determine if the Omicron is well covered by the third dose and for how long," Bourla added. "And the second point, I think we will need a fourth dose."
On Tuesday, the Pfizer CEO said he was concerned about how fast the Omicron variant is spreading.
"I don’t think it’s good news to have something that spreads fast,” Bourla told the Wall Street Journal. "Spreads fast means it will be in billions of people and another mutation may come. You don’t want that."
Bourla said he expects the number of Omicron cases to balloon from dozens to millions over the next few weeks.
A study in Japan found that the Omicron variant is 4.2 times more transmissible than Delta, Bloomberg reported.
"We will have a good understanding, let’s say before the year end, as to what exactly it means for clinical manifestation," Bourla said.
He said that Pfizer could develop a vaccine that targets Omicron by March 2022, but the pharmaceutical giant is still determining whether the current vaccines provide protection against the newest variant.
Bourla also said, "A third dose will give very good protection, I believe."
BioNTech and Pfizer claimed in a statement Wednesday that three doses of their COVID-19 vaccine were "able to neutralize the new omicron variant in a laboratory test." The press release also said, "Two doses of their vaccine resulted in significantly lower neutralizing antibodies but could still be protective against severe disease."
BioNTech chief medical officer Ozlem Tuereci said two doses of the vaccine "might be compromised," but added, "Three doses of vaccination are required to restore protection."
Dr. Rochelle Walensky — director of the Centers for Disease Control and Prevention — told the Associated Press that "the disease is mild" in almost all of the cases thus far. Reported symptoms mainly were cough, congestion, and fatigue. CDC officials said one person was hospitalized with the Omicron variant, but no deaths have been reported.
"As of Wednesday afternoon, the CDC had recorded 43 cases in 19 states," the AP reported. "Most were young adults. About a third of those patients had traveled internationally."
Walensky said that more than 75% of the patients infected with the Omicron variant had been vaccinated, and a third had received boosters.
The CDC stated, "Current vaccines are expected to protect against severe illness, hospitalizations, and deaths due to infection with the Omicron variant. However, breakthrough infections in people who are fully vaccinated are likely to occur. With other variants, like Delta, vaccines have remained effective at preventing severe illness, hospitalizations, and death."
The Omicron variant — initially known as the B.1.1.529 variant — was first identified in South Africa and was reported to the World Health Organization on Nov. 24.
Bourla said he expects next year to be more normal as long as "a variant that changes everything" doesn't appear.
"I think we were in a good path mid of next year to be having things under control," he stated.