Definitions
(taken from Cambridge Dictionary)
voracious: very eager for something, especially a lot of food
lionize: to make someone famous, or to treat someone as if they were famous
voluble: speaking a lot, with confidence and enthusiasm
diurnal: being active or happening during the day rather than at night:
Because the only definition having something to do with desire/eagerness is for voracious, this is the word that means "excessively eager".
Answer
voracious