The One Way Road and South Rim trails are both closed to visitors until the threat is deemed to have passed.
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Rangers could reopen the trails by Monday if they don't find any additional signs of the mountain lions, according to city officials.
Rangers have confirmed the sightings of one or more lions over the past five to seven days, one of which was spotted just a couple of feet from the One Way Road Trail around 5:15 p.m. Wednesday.
"This (lion has) been seen repetitively, roughly in the same area," Park Ranger Pam Helmke said. "We don't know why he or she is hanging around."
VIDEO: Mountain lion caught on camera dragging deer off Hillsborough porch
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Mountain Lion caught on camera on Hillsborough porch
It could be that the lion has a deer carcass stashed in the area or it could be that it doesn't have its own territory yet and is just resting at the park as it moves through the area, Helmke said.
"Whenever they get close to where humans might be, that's a danger," Camarena said.
Rangers advise people who encounter mountain lions to keep away from them since they may feel cornered if approached.
People who find themselves in close proximity should stand tall and face the lion without turning their backs to the animal. They should make as much noise as possible and try to look as large as possible by waving their arms or throwing objects.
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People with small children should pick them up without bending over, according to park officials.
Mountain lions are a protected species in California and many live all around Santa Clara County.
Their primary food source is deer, but they also prey on smaller animals like raccoons, rabbits, and feral pigs.
Anyone encountering a mountain lion at Alum Rock Park should call the ranger office at (408) 259-5477.
Alum Rock Park trails closed after Mountain Lion sighting