what is the most appropriate tense in the following context:

Mr Jones asked Mr Brown: "Have you spoken to your wife already?"

"No, she wasn't there when I phoned. My small son answered the phone. I asked him, "Is your mother there?" And he said, "She is somewhere outside".

"Why is she outside?" I asked. "She was looking for me", he answered.

The book says the right answer is "was looking" but in my opinion "has been looking" fits even better.

Thank you for your answers.
She was looking for me fits better although I would suggest with either of these tenses she would be home now. I would expect, "she is looking for me." That would explain why so isn't at home.
I see. But would you say these phrases - was looking and has been looking are definitely wrong in this context?

This is an old exam task actually. Not a good one, though - greetings to Moscow!
Students: Are you brave enough to let our tutors analyse your pronunciation?
Any ideas?
None of them are definitely wrong as they sentences are structured properly. The question is what is more likely in the context and I have given you my answer, and the thought process behind it.