A deal between Apollo Global Management and Apollo Education could be reached in the next few weeks, the Journal reported.
Apollo Education and rivals such as DeVry Education Group and ITT Educational Services have faced tougher regulation since a series of government investigations in 2010 revealed low graduation rates and poor job prospects for graduates, who were also burdened with high student debt.
Stricter funding rules from the U.S. Department of Education have also squeezed federal tuition aid, which has been a major source of revenue for the for-profit education providers.
The U.S. Department of Defense put the University of Phoenix on probation in October, barring it from recruiting students on military bases or using federal money to fund tuition.
The decision followed investigations by the U.S. Federal Trade Commission and the state of California, which are ongoing.
The FTC, in July, demanded information about the university's marketing and advertising techniques, which it said may have been deceptive.
The California attorney general's office issued a subpoena in August, seeking information on recruiting of military and National Guard personnel and the use of military logos and emblems in marketing.