having one's eye on

Verb

have one's eye on (third-person singular simple present has one's eye on, present participle having one's eye on, simple past and past participle had one's eye on)

1. Used other than figuratively or idiomatically: see have, one's, eye, on.

   Synonyms:

   have designs on

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

   Synonyms:

   keep an eye on

3. 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 December 14, Angelique Chrisafis, “Rachida Dati accuses French PM of sexism and elitism”, in Guardian