have one's eye on

verb2

1. •
   To watch.

   • I have my eye on you, so you'd better not cause any trouble.
2. •
   To seek, to pursue.

   • She now wants to be a Paris MP. But Fillon wants the same Paris seat when he steps down, after next year's election. Both have their eye on the main prize: running for Paris mayor in 2014. — 2011