In the Ocean of Night

From the back cover Warner paperback February 2004:

2019: NASA astronaut Nigel Walmsley is sent on a mission to intercept a rogue asteroid on a collision course with Earth. Ordered to destroy the comet, he instead discovers that it is actually the shell of a derelict space probe -- a wreck with just enough power to emit a single electronic signal...

2034: Then a reply is heard. Searching for the source of this signal that comes from outside the solar system, Nigel discovers the existence of a sentient ship. When the new vessel begins to communicate directly with him, the astronaut learns of the horrors that await humanity. For the ship was created by an alien race that has spent billions and billions of years searching for intelligent life... to annihilate it.

Synopsis from Open Library.