The United Federation of Teachers says those are the numbers needed to open middle and high schools safely next week.
So far, the city has committed to hiring 4,500.
Albert Einstein School in the Bronx, reopens Wednesday after it had two cases of COVID-19 within a week.
In the city, 14 schools are reporting at least one confirmed case of the virus between last Friday and Monday.
Officials say 65 teachers have tested positive out of more than 19,000 who participated in testing.
Monday was the first day of school for the city's 1.1 million students either working remotely or in-person.
While more than one million students attended online, about 90,000 younger and special education students headed back to their classrooms for in-person learning.
Mayor Bill de Blasio said more teachers might be needed, but he couldn't give an exact number.
He said that's because parents continue opting their kids in and out of in-person learning, and some teachers are also opting out of in-person instruction.
There is a "real heavy emphasis on the cleaning, the ventilation, the PPE, any last minute problems being addressed really quickly, and then making sure the staffing is moved where it needs to be," de Blasio said.
RELATED: Stay informed with ABC7's NYC COVID-19 positivity rate tracker
MORE INFO: NYC Department of Education
Here are the city's current back-to-school details:
On Monday, 3-K, Pre-K, and early education sites will open including District 75 for special education.
Children who are enrolled in fully remote programs will still begin full-day instruction.
Children in blended learning will be learning remotely until their in-person start date.
All Elementary Schools (K-5 and K-8) including students in Grades 6-8 in K-8 schools: In-Person Learning begins on Tuesday, September 29
Middle Schools (Grades 6-8): In-Person Learning begins on Thursday, October 1
High Schools (Grades 9-12): In-Person Learning begins on Thursday, October 1
Secondary Schools (Grades 6-12): In-Person Learning begins on Thursday, October 1
Transfer Schools, Adult Education, Evening Schools: In-Person Learning begins on Thursday, October 1
K-2 and K-3 Schools: In-Person Learning begins on Tuesday, September 29
Stay informed with ABC7's NYC COVID-19 positivity rate tracker
Grades K-8: In-Person Learning begins on Tuesday, September 29
Grades 9-12: In-Person Learning begins on Thursday, October 1
RELATED: New York, New Jersey, Connecticut out-of-state travelers quarantine list
MORE CORONAVIRUS COVID-19 COVERAGE
Back to school information
How coronavirus changed the New York region
Do you have coronavirus symptoms?
What's Open, What's Closed in the Tri-State area
COVID-19 Help, Information. Stimulus and Business Updates
New York City
Westchester and Hudson Valley
abc7NY Phase Tracker: