Aerojet Rocketdyne Holdings Inc. has bid about $2 billion for United Launch Alliance, a joint venture of Boeing Co. and Lockheed Martin Corp. struggling to maintain its position as the premier supplier of rockets to the Pentagon, according to people familiar with the matter.

The two sides are in advanced talks about what one of these people described as an all-cash offer. A deal hasn’t been finalized, and could be derailed by last-minute hurdles. Any such deal would be subject to close analysis by Pentagon officials, the...