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lick one's lips
Fig. to show eagerness or pleasure about a future event. (From the habit of people licking their lips when they are about to enjoy eating something.) The children licked their lips at the sight of the cake. The author's readers were licking their lips in anticipation of her new novel.
lick your lips
to feel pleased and excited about something that is going to happen, usually because you think you will get something good from it Meanwhile, the property developers are licking their lips at the prospect of all the money they're going to make.