From Longman Dictionary of Contemporary Englishdrift off phrasal verbSLEEPto gradually fall asleep I was just drifting off when the phone rang. He felt himself drifting off to sleep. → drift→ See Verb table
Examples from the Corpus
drift off• He must have drifted off again, for when he awoke, the train had come to a halt.• That night as he drifted off to sleep, Quincy tried to imagine what the day would have been like if Marta had been there.• She was just starting to drift off, when she heard a scream downstairs. 