have an eye on something—
1. choose smth. one has seen as a desirable acquisition:
- I have had an eye on a dress in the shop across the road for some time.
2. keep close watch upon smth.:
- The chances are that the authorities may have had an eye on such kind of “hardware” [torpedoes].
3. pay careful attention to smth.; show concern for smth.:
- Truly successful companies have had an eye on quality for decades.
have one eye on something—give only part of one’s attention to smth. while the rest is engaged elsewhere:
- It was a tricky experiment—he had to have one eye on the thermometer all the time.