have one's eye on

have one's eye on

1. Used other than with a figurative or idiomatic meaning: see have,‎ one,‎ 's,‎ eye,‎ on.
2. To watch.

   I have my eye on you, so you'd better not cause any trouble.

3. To seek, to pursue
   • 2011 December 14, Angelique Chrisafis, “Rachida Dati accuses French PM of sexism and elitism”, in Guardian‎:

     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.

• have designs on