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
have an eye to. Have as one's objective, as in We had our eyes on that birthday cake, or The Republicans have an eye to a big majority in the House. The first usage dates from the mid-1600s, the second from the early 1500s.
with an eye to. With a view to, regarding as an objective, as in With an eye to her inheritance, she was very attentive to her aunt.