Question

She said to me,"may i use your pen convert this into reported speech

Answer 1

May expresses primarily possibility and, secondarily, permision and volition. In seeking permission, as in your examples, the use of may is much more formal and polite than can and is used rather less. However, both 'Can I have your pen please?' and 'May I have your pen please?' are blunt ways of making a request.

Answer 2

Answer:

he asked me if he can use my pen