Schools Chancellor Dennis Walcott said yesterday he’s hopeful that layoffs can be averted, but still can’t tell anxious teachers whether they will have jobs in September.

“I’m an eternal optimist by nature, so I hold out hope,” Walcott told The Post at a gathering of the Queens alumni chapter of the Alpha Phi Alpha fraternity, a group that gives out scholarships.

City Hall is in talks with the teachers union over Mayor Bloomberg’s threat to lay off 4,100 educators.