put (one's/someone's) name in the hat
To submit one's own or someone else's name for consideration in a selection, such as a competition, application pool, election, etc. I'm thinking about putting my name in the hat for class president! Just so you know, I put your name in the hat for a chance to win an all-expenses-paid trip to Florida! As has been widely predicted, the governor announced today that he was putting his name in the hat for the presidential election next year.