Monday was the deadline for private and community groups to apply for a chance to oversee 30 district schools.
Villaraigosa's nonprofit group, which already manages 11 schools, as well as other groups backed by the teachers' union, will compete for control of four of those campuses.
Superintendent Ramon Cortines will make the decision.
The reform plan could ultimately allow private groups and charter school operators to take control of around 250 new or low-performing schools. That is about a third of the number of schools in the LAUSD.
The Associated Press contributed to this story.