Given how vast the universe is and how long it would take to reach any planet with intelligent life, he said it's unlikely that humans will encounter aliens face to face in space.
He also said that since humans only started leaking radio and television broadcasts into space since World War II, it's unlikely that aliens know we even exist.
But he said that it's possible humans could encounter artifacts left by aliens billions of years ago, before humans had evolved.
"They might have left a message in a jar -- a time capsule," he said. In the movie "2001: A Space Odyssey," for example, the message was left on the moon.
He also said it's possible, although highly unlikely, that aliens might visit randomly.
"I think that's unlikely because, again, they don't know we're here, so it would be extraordinary if they visited now," he said.
A more plausible scenario, he said, is that SETI, which uses radio telescopes and optical telescopes to listen for signals of technology from extraterrestrial life, could detect life on another planet.
So far, after more than 40 years, there has not been a peep. But SETI's technology is advanced enough that it can detect signals from up to 1,000 light-years away, which includes a zone with about one million stars. A signal could have been sent 1,000 years ago, before that civilization had any knowledge of Earth.
"The idea of aliens, that's an old idea. I'm sure every society has had some people that look up at the sky and gaze and wonder if there's someone looking back this way," Shostak said.
Even though we're not at a point in history when we could surf the galaxy and search for aliens, he said, "What we are able to do now is actually maybe find them, to at least know that they're out there."