WordNet (r) 3.0 (2006):

keep an eye on
    v 1: follow with the eyes or the mind; "Keep an eye on the baby,
         please!"; "The world is watching Sarajevo"; "She followed
         the men with the binoculars" [syn: watch, observe,
         follow, watch over, keep an eye on]

Moby Thesaurus II by Grady Ward, 1.0:

66 Moby Thesaurus words for "keep an eye on":
   attend to, au courant, baby-sit, be vigilant, be watchful, boss,
   care for, chaperon, cherish, conserve, eye, eyeball, follow,
   foster, gaze at, have a looksee, hold in view, keep account of,
   keep count of, keep in order, keep in sight, keep in view,
   keep informed, keep posted, keep track of, keep under observation,
   keep up on, keep watch over, look after, look at, look on,
   look out for, look to, look upon, matronize, mind, minister to,
   mother, nurse, nurture, observe, overlook, oversee, preserve,
   protege, provide for, reconnoiter, regard, ride herd on, scout,
   see after, see to, shepherd, spy upon, stand over, stay briefed,
   superintend, supervise, support, take care of, take charge of,
   tend, view, watch, watch out for, watch over