Step 1: Alternative construction:
Direct questions using auxiliary verbs (like 'will') are reported using 'if/whether' as the connector.
Step 2: Applying the shift:
'tomorrow' changes to 'the next day' since the reporting is not happening on the same day; 'me' changes to 'him' (third person).
Step 3: Final Answer:
He asked the teacher respectfully whether he would not teach him the following day.