- A secretive, pining look, or humble doting glance.
1864, Joseph Addison, The Spectator, number 250:
- those of an amorous roguish look derive their title even from the sheep, and we say such a one has a sheep's eye, not so much to denote the innocence as the simple slyness of the cast.
1875, Anthony Trollope, Never, never, -- Never, never: A Condensed Novel in Three Parts, after the Manner of Bret Harte:
- He had ever a sheep's eye for thee, and, if I remember rightly, thou wast sweet upon him once.
- 2013, A Scott Berg, Wilson, Berkley 2014, p. 400:
- No less an eminence than former President Taft himself (who had long cast a sheep's eye on the high court) privately called the nomination “one of the deepest wounds that I have ever had as an American and a lover of the Constitution and a believer in progressive conservatism.”
Often used in plural. Sometimes "to cast a sheep's eye" or "throw a sheep's eye" on someone.
a secretive, pining look, or humble doting glance
-  Miriam-Webster's Collegiate Dictionary
-  "The Gaelic etymology of the languages of western Europe: And more especially of the English and Lowland Scotch, and their slang, cant, and colloquial dialects". By Charles Mackay.
-  "The Works of Joseph Addison Complete in Three Volumes Embracing the Whole of the 'Spectator,'" &c. By Joseph Addison.
-  "Never, never, -- Never, never: A Condensed Novel in Three Parts, after the Manner of Bret Harte". By Anthony Trollope.