At a hearing Sunday morning, San Francisco Superior Court Judge Curtis Karnow indicated that he would grant Gov. Jerry brown's request for a 60-day cooling-off period.
Brown's request came after a panel appointed by the governor to investigate the labor dispute concluded that a strike would cause significant harm to the public's health, safety and welfare.
A formal order granting the injunction was expected later in the day.
This means Bay Area Rapid Transit trains would keep running while negotiations continue.
The talks began four months ago. BART and its two largest unions are trying to agree on wages, pensions and health care benefits.
BART, the nation's fifth-largest rail system, serves more than 400,000 commuters each weekday.
The Associated Press contributed to this report.