I am not sure what your questions is, because qualitative interviews are always composed of a series of open-ended questions. Can you tell us more about your research questions and goals?
Yes, open-ended questions are the main data collection tool in qualitative approach that allows indepth understanding of phenomenon under study.
Formulating the questions, techniques of asking, attention to non verbal responses, and selecting of subjects are essential considerations for successful study.
I mean while an interview is administered orally, the open-ended questions I want to refer here is a question that is administered in a written form( given to respondents to write their response)
Do you mean a questionnaire with open-ended questions, which your participants will fill-in their responses. If so, yes, you can use that in a qualitative research. The challenge is that you will get little depth.
If you are interested in using a qualitative questionnaire with open-ended questions and spaces for participants to fill-in their responses, that is very possible. After administering the questionnaire to your participants, you can code and analyze the date using content thematic analysis. Depending on the responses, you can undertake deductive coding (you apply a predeveloped coding frame to organize the data) or inductive coding (you develop new codes from the participants' responses). You need to be clear about why and how you perform your coding and further analysis thereof. When using content thematic analysis, you start with content analysis to determine the counts of similar responses to create content categories, which you will develop further into thematic categories (themes). The themes become the sub/headings in your results section under which you describe, explain, and interprete the participants' perspectives.
Written open ended questions in form of questionnaire can be used in qualitative data collection because they allow participants to express themselves and go deeper into the phenomena, they can save you time and resources. However, you can miss out some details you would get through verbal follow up questions.