i always say (after getting to manager)
Hi first name, Josh Ferencz, i had a chance to meet you last week when i turned in an application, just wondering if you had had a chance to review it yet, and was wondering if we could set up a more formal meeting when you have a chance..."
this lets him remeber you having met, and shook his hand firmly. review the application is strong confident and well worded without going over board. asking to set up an interview acknowledges you understand when you first met he was probably in a hurry, because you expect to be busy while working. and lastly you dont wait for him to offer or say when interviews are, you are the one pushing for the invite.