When Russians supposedly detected signals from space in 1965, Kubrick and Clarke reached out to a contact at The New York Times to find out if the news was accurate. It turned out the signals were just pulses from a quasar. Then Kubrick, already building a reputation for worrying about things that wouldn't even occur to normal brains, contacted Lloyd's of London to buy an insurance policy that would pay out if NASA found aliens, protecting himself against 2001's presumed resultant failure. Lloyd's is famous for unusual policies (whenever you hear a news story like "Sony has insured Zach Galifianakis' beard for $1.2 million," they probably did that through Lloyd's), so he'd gone to the right place.
They actually agreed to issue a policy. But they evidently rated the chances of NASA finding aliens pretty high (or thought Kubrick had some inside info?), because they demanded a premium that was "slightly astronomical," as Clarke put it. Kubrick couldn't afford it. He was still unsure how to portray aliens without looking silly when NASA inevitably discovered Transformers, but at some point, pal Carl Sagan posited that maybe they could just not show aliens at all. If they suggested aliens instead of depicting them, they could never be proven wrong. So in the end, that's what they went with. Cowards.