It might be nothing, but I'd like you to keep a discreet eye on him, if you can.
And, of course, it also means you'll be able to keep a discreet eye on how your tenants are treating your property.
You asked me a couple of months ago to keep a discreet, apart from an official, eye on them.
The burgemeester, who was really rather a dear, allowed a discreet eye to rove over her person.
Hotel employees try to keep a discreet eye on guests' health not just when they check in but during their stay as well.
Kestrel asked nervously, keeping a discreet eye out for anyone who might be following or listening to them.
And we'll keep a discreet eye on him.
She kept a watchful, if discreet, eye on Brennan since he entered the shop.
You stay here and keep a discreet eye on him.
Someone would keep a discreet eye on the unmilitary major to make sure he did what he was supposed to do and nothing else.