The bear can see the hunter´s rifle and is begging for mercy. The hunter speaking to his companion: "The bear is asking me not to kill him."

  You must be careful because ask can be used to report questions and requests and the reported clauses are different in each case.

Suggestions are often reported by means of: the verb suggest:

Paul to his girlfriend: Why don´t we go to the cinema?

Paul´s girlfriend to her mother: Paul suggested going to the cinema.