I wonder, should I?
-(으)ㄹ 까요? is used when the speaker wants to make a suggestion to the listener or to ask the listener for his or her opinion.
The subject is normally 제가 or 내가 and may be omitted.
In English, this expression corresponds to 'Shall I...?' or 'Do you want me to...?'
When responding, the imperative forms -(으)세요 or -(으)지 마세요 can be used.
When the verb stem ends in a vowel or ㄹ, -ㄹ 까요? is used, and when the verb stem ends in a consonant, -을 까요? is used.
Wondering to oneself, considering a possbility or action.