have (someone or something) in (one's) sights

1. Literally, to have one's gun aimed at someone or something. I had the deer in my sights, but I stepped on a branch and scared it away. The snipers have the target in their sights, sir. It was unbelievably terrifying—I didn't know anyone had me in their sights until I heard the gunshots!

2. By extension, to intend or be preparing to attack or defeat someone. He's had a phenomenal career for such a young boxer, and now he has the reigning champion in his sights. Be careful. You don't want a company like them to have you in their sights. He has the CEO in his sights for his next big exposé.

3. To be focusing one's attention and desire on obtaining or achieving something. They've had an Olympic gold medal in their sights for the last eight years. The retired actor now has public office in his sights. Ever since she was a little girl, Janet has had her sights on being a fighter pilot.

have someone in your sights

If you have someone in your sights, you are determined to catch or defeat them. Note: The sights on a weapon such as a rifle are the part that helps you to aim it more accurately. Knight had Thomas in his sights for much of the race, but in the end, failed to catch him up. Lennox Lewis beware! Earl Barrett has got you in his sights. Note: These expressions are often used more literally to say that someone is looking at a target through the sights of a gun.