have one's eye on

English edit

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)

Used other than figuratively or idiomatically: see have,‎ one's,‎ eye,‎ on.
To watch.
I have my eye on you, so you'd better not cause any trouble.
To seek, to pursue.
- 2011 December 14, Angelique Chrisafis, “Rachida Dati accuses French PM of sexism and elitism”, in Guardian‎^[1]:
  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.

idioms meaning "to seek, pursue"

watch — see watch