With wary eyes cast toward smoke-filled skies and down at Air Quality Index readings, Cal, Stanford and Pac-12 Network officials Thursday were holding out hope that Saturday’s Big Game still will be able to be played as scheduled.

But there was growing concern that — for the first time in more than 50 years — the annual game between the Bay Area rivals might have to be postponed in the wake of the Camp Fire in Butte County.

Kickoff is scheduled for 4:30 in Berkeley’s Memorial Stadium.

In a statement late Wednesday, Cal Chancellor Carol Christ said that if the AQI on campus surpasses 200, game cancellations are considered.

At 4 p.m. Thursday, the AQI in Berkeley was 232, which led to the cancellation of Thursday night’s men’s basketball game against Detroit Mercy at Haas Pavilion. Late Thursday, the university also announced the cancellation of all classes Friday. Friday’s on-campus, unveiling of a plaque honoring former quarterback and head coach Joe Kapp also was called off.

In San Francisco, USF said that Friday night’s men’s home basketball game against Arizona State has been postponed. Athletic director Scott Sidwell said he and counterpart Ray Anderson of ASU were working to find a replacement date that works for both teams.

This year’s is the 121st Big Game. The only years since 1892 in which it hasn’t been played were during World War I (1915-18) and World War II (1943-45). The 1963 Big Game was postponed a week after the assassination of President John F. Kennedy.

In her statement, Christ said, “The Bay Area Air Quality Management District is forecasting a significant improvement in air quality beginning on Friday morning, with continued clearing throughout the weekend. We will continue to closely monitor reliable readings and forecasts and will keep the campus community updated.”

On Thursday, AQI numbers throughout the Bay Area soared. According to sparetheair.org, the AQI in Berkeley was forecast to be 182. It got that low for three hours (8-10 a.m.), but then reached as high as 247 at 3 p.m., according to the BAAQMD’s website.

Cal Athletics said it is in regular communication with officials from the Pac-12 and will take appropriate measures.

A Cal athletic-department official said that, as of Thursday night, no play/don’t-play deadline had been established.

“Stanford Athletics is continuing to monitor the Air Quality Index, as outlined in our sports medicine and NCAA policies,” Stanford said in a statement. “At this time, there are no changes to our weekend schedule, which includes six events hosted on campus starting Friday. Additionally, we remain in contact with officials from (Cal) and the Pac-12 in regards to the status of Saturday’s Big Game.”

Unlike the 1963 game, a postponement of this year’s Big Game likely would be more than a week. Cal (against Colorado in Berkeley) and Stanford (at the Rose Bowl against UCLA) both play Nov. 24 to end their regular seasons.

Neither Cal nor Stanford will be in the Pac-12 championship game — which will be played Nov. 30 (a Friday night) at Levi’s Stadium — so it’s possible that a delayed Big Game could be pushed back to the next day, Dec. 1.

Rusty Simmons and Mike Lerseth are San Francisco Chronicle staff writers. Email: rsimmons@sfchronicle.com and mlerseth@sfchronicle.com Twitter: @Rusty_SFChron and @MikeLerseth