shall in reported speech

The following question is to be put into reported speech:

"Shall I ask her out for a meal?"
Suggestion:
He has has been wondering whether to ask her out for a meal.

How do I go on if the sentence starts like this:

He has has been wondering whether he ......

Is it "shall / is to / is supposed to / should /was to / was supposed to ?

I'd prefer "should" but I may be wrong.

What do you suggest?

hilti955

You are right, should is OK.

I would say it this way:
He was wondering whether he should ask her out for a meal.