The phrase "an eye on something" is correct and usable in written English.
It is typically used to indicate that someone is watching or monitoring a situation or object closely.
Example: "The manager kept an eye on the project to ensure it stayed on schedule."
Alternatives: "monitoring something" or "keeping watch over something".
As soon as I set an eye on the thing, however, something shot up from the metal window sill, like an electron thrown out from a sheet of radium, and I thought: I know this place – I've stayed here before.
Simeone crept from room to room looking for the problem phone in question: She checked the office, checked the "viewing room" where they keep an eye on the seals, checked something called the "fish kitchen," but at each turn, she found nothing.
He has his eye on something called a Slow Chair, a high-design item made by two French designers for Vitra, he said, but it is $3,459.
"If you've had your eye on something for a while and want to make a lowball offer, do it now".
"If I'm reading an email I've always got my eye on something else," says Usher. "But if a letter comes through the door, I'm always in awe that someone has taken the time and made the effort.
In 1999, Riley "had her eye on something called a 'Prius', already available in Japan"; nine years later, on page 301, Janet is "thankful that Jonah drove the old Prius" – I don't think it is mentioned in between.
It's also a good idea to have someone keeping an eye on you, just in case something goes wrong.
When I went back into her room, I was told to keep an eye on the monitor and say something if her heart rate sank below forty.
She was obsessed with accessories from the earliest age and used to wander the aisles at the original Loehmann's, in Brooklyn, where, she said, the founder kept an eye on her: "She looked like something out of Toulouse-Lautrec, and she would sit on a high stool like she was observing a tennis match and she would look at what everybody in the shop was doing….
