The review process could move past that date, The Times said, as paperwork and negotiations with the company continue.
The move would make it the first vaccine to go from emergency use authorization to full FDA approval.
The FDA declined to comment on the Times report to CNBC.
Pfizer and BioNTech initially began the process of applying for their biologics license for the two-dose vaccine in May after receiving emergency use authorization from the FDA last December. The FDA sets a six-month target for approving high-priority drugs and a 10-month target for all other standard drugs.
The companies announced Monday that they began the approval process for their third booster dose after submitting clinical trial data to the FDA.
Top health officials from agencies including the CDC and FDA said in a statement Wednesday that the effectiveness of mRNA vaccines declines over time, especially for those with compromised immune systems or for anyone inoculated early in the vaccine rollout.