after at least 5 years of being a pr, you can apply for naturalization, and it will take another year or so for application to wait in queue, processing, written test to be taken and finally oral test via a face-to-face interview at the nearest immigration office. after the interview, it will require months for processing, approval, oath-taking and issuance of naturalization certificate. the latter 2 events are done concurrently at a swearing-in ceremony where the cert is presented at the end of the ceremony. there's no such thing as a "citizenship offer." you either apply for it or you don't.