The two ways of relating what a person has said are 1)direct and 2)indirect (reported).

In the direct speech, the exact words of the original speaker are repeated.

In the indirect speech (reported speech), the exact meaning of what the speaker told is expressed but not necessarily in the speaker’s exact words.

Option C is correct as the question in the inverted commas is in the simple present tense and 'may'  is used with the first form of 'use'.

Options A, B, and D are wrong as the meaning of the sentence is changed, the telephone didn't belong to the person who requested to use it, and the telephone belonged to the person whom the speaker of the question asked respectively.

The correct answer is C)he might use my telephone.