watch like a hawk - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Observe very closely, as in I was watching him like a hawk, but I never did see him take your wallet. This simile alludes to the hawk's exceptionally keen sight.