Chicago public school teachers and their supporters rally at the school district's headquarters earlier this week. (CNN)
CHICAGO (CNN) -- A tentative deal has been reached in the dispute between the Chicago Teachers Union and the city's school board, a source with detailed knowledge of the strike negotiations said Friday.
Students could be back in the classroom as soon as Monday, according to the source.
New hope emerged Thursday after days of sometimes contentious meetings between the teachers union and the school board.
"We will see if we can finish this up, hopefully, tomorrow," Chicago School Board President David Vitale told reporters Thursday night. "I think we made some pretty good progress."
Schools remained closed Friday, the fifth day of the strike, amid the negotiations.
Chicago Teachers Union spokeswoman Stephanie Gadlin said union delegates with the power to stop the walkout would be meeting Friday afternoon.
The union, which represents nearly 30,000 teachers and support staff, called the strike on Sunday night.
The union has said the two sides had been close to a deal on pay, but far apart on teacher evaluations, benefits and other issues.
Teachers are concerned about job security in the wake of a new program that evaluates them based on their students' standardized test scores. Chicago Teachers Union board member Jay Rehak called the program "data-driven madness."
As many as 6,000 teachers could lose their jobs under the evaluation system, said union President Karen Lewis, who called the system "unacceptable."
The mayor's office, the city and school officials have questioned that job-loss figure.
The median base salary for teachers in the Chicago public schools in 2011 was $67,974, according to the system's annual financial report.
Parents have been anxious for a resolution of the strike.
"There is ... frustration, foremost," said Sarah Liebman, the mother of two children in city schools. "It's really affecting the kids right now."
Ahead of the strike, the Chicago Public Schools crafted a plan -- one criticized sharply by union leaders -- trying to give parents like Liebman options until teachers return to work.
The city's famed public transit system offered free rides for students to move between so-called "safe haven" sites.
Chicago's parks department resumed camp-style sports, art and nature programs at dozens of its locations, while the public library system set aside computers in its facilities for students to use.