The contractor is asking for approximately $500,000 in additional funds to repair air ducts on the school's roof, but the school board is willing to pay just $100,000.
The English Montreal School Board (EMSB) said most of these extra costs were covered by the initial contract.
In October, school authorities said John F. Kennedy High School in Montreal's Saint-Michel borough was on track to reopen on Jan. 7, but the spokesman for the EMSB, Michael Cohen, said they might have spoken too soon.
He said there is a dispute between the school board and the contractor.
"When it comes to construction of this magnitude, there are never any guarantees," said Cohen.
Since the school's closure, students have been sharing space at nearby Rosemount High School but some students find it stressful to study in a different environment.
"It's been very difficult because we haven't been able to concentrate on our work. We're too busy concentrating on our surroundings," said Carol-Anne Daigle-Constantini, a student at John F. Kennedy.
She said another delay would simply create more stress for students. She also said the board might want to consider waiting until next fall before reopening the school.
The school board said it is trying to resolve the dispute out of court, but legal action remains an option.
The EMSB should have an update on possible construction deadlines by next week.