Also, keep an eye on. Look at, especially attentively or continuously; watch. For example, The teacher has his eye on the boys in the back row, or Please keep an eye on the stew. [First half of 1400s] Also see keep an eye out for.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.