A resident was in his backyard with his wife at about 7 p.m. when he saw two deer running through San Ramon Creek, Lt. Jeff Moule said.
About five minutes later, the man saw what he believed to be a mountain lion heading in the opposite direction.
The resident, who Moule described as a knowledgeable outdoorsman, said he guessed that the cougar had chased the deer, but didn't catch them and was heading back to its territory.
The man said that he wasn't entirely sure what he saw was a mountain lion, but described the animal as brown, with a long tail and weighing more than 100 pounds.
Police have informed the state Department of Fish and Game about the sighting and flyers will be posted at the entrances to the park to warn people of the possible sighting.
The flyers will also provide tips of what to do in case a mountain lion is seen.
People should not approach a mountain lion. If a mountain lion is seen, people should not run. They should pick up small children, face the animal and make noise.
People should also avoid biking, jogging or walking alone, especially at dawn, dusk or night.
Moule said that a mountain lion was seen in a similar area in 2008 and officials from the Department of Fish and Game said it most likely came from an open space area to the east and was hunting along the creek.