You mention both "qualitative inquiry" and "qualitative research" but not qualitative methods. I think it is quite possible to use qualitative methods within a positivist paradigm. For example, you could do comparative case studies, where you have hypotheses about the cases will differ, and you collect qualitative data to test those hypotheses.

I'm thinking with professor Morgan. You can use case studies (see Eisenhardt 1989 or Robert Stake 2001, for example), but you can use focus group or action research too. This definition usually happens from your starting point, positivist research is not necessarily conflicting with qualitative research methods. 

See Eiseinhardt's article in this site:

https://www.jstor.org/stable/pdf/258557.pdf?_=1470073323644

I think there are very few positivists these days in academia, and most are post-positivists. Hence lets address your question from a post-positivist view (though it is true for positivist as well). The answer is yes, and it is sufficient to look at Glaser and Strauss whose initial version of grounded theory was very much post-positivistic.

What David said is then of course very true. Qualitative methods can b used to test theories and hypotheses as they are good for generating them. What makes qualitative methods unique, in my eyes, is that they seek to identify qualitative attributes of phenomena rather than quantitative. Whether or not the researcher perceives his/her findings as actual entities in reality changes very little in this respect. Moreover, even a constructionist researcher as myself may not control the manner in which readers understand the necessary reservations accompanying the study, and hence, the study may always be understood in positivist eyes. If this is the case, then surely it may also be carried out from that epistemological (if not methodological) perspective.

I would agree with Jacob.  The post-positivist (like the positivist) still adopts the stance that there is a 'truth' independent of the researcher, and the researcher seeks to identify that 'truth' - albeit in the social sciences the 'truths' may be socially constructed and identified by a social consensus. Therefore if you are seeking to obtain data from informants and are not seeking to a) construct truths with the aid of your informants (so your questioning tends to simply eliciting responses without overmuch probing)  or b) seeking to empower informants by making them aware of, say, power structures (i.e. adopting a frame of critical analysis) - then generally you are working in a post-positivist paradigm - something that may then be reinforced if you use textual software to analyse underlying dimensions. As an aside - I tend to a view that mixed methods research tends to drive the researcher into a  post-positivist paradigm, but that is an argument for other times! Coming back to my original point - it may also mean that you are still tending to work in the initial descriptive stages of research (i.e what do your informants think) prior to seeking why do they think that way. This is where boundaries tend to get blurred and fuzzy, and, in my experience, social science research as a process is often crossing such boundaries between definitions.

Dear Salman

If you want to know if is it possible to use quantitative methods in a positivist paradigm as Professor Morgan said above I guess this quote of Yin (2003) may be useful to answer your question.

“You can also use multiple strategies in any given study (e.g., a survey within a case study or a case study within a survey). To this extent, the various strategies are not mutually exclusive”.  

Thanks to Professor Morgan, Carlos Chaym, Jacob, Chris Ryan and Yves Netto for your contributions

I do not believe that it is possible follow the tenets of a positivist philosophy in quantitative social science research - I argue the case here 

https://www.researchgate.net/publication/256801634_The_practice_of_quantitative_methods

Chapter The practice of quantitative methods

I would also suggest the use of Appreciative Inquiry: 4-D model: 1Discovery - appreciating the program, 2Dream - envisioning the results, 3Design - constructing the future, 4Destiny - sustaining the change. Meeting agenda, interview guides and summary sheets could be developed for a succesful focus group meeting while collecting qualitative data. AI is used as a development process( in many situations) that focuses on positive and creative factors for a better future. AI suggests to look at opportunities and strengths while drawing on the hopes of people.

If one thinks of positivism as 'objective truth' (and yes, I know that's simplistic but this a Q&A), WHY would you want to use a qualitative approach?

You might want to use qualitative approaches because it may answer questions that cannot be answered otherwise. Emic questions in opposed to etic questions, for instance. That said, approaching such questions from  positivist epistemological and ontological premises will result in a non-reflexive study which fails to take into account the researcher as a constructor of knowledge, and of course overlook the "fact" that the participants are as well, and that both are situated within traditions of knowledge which constrain their interpretations of reality. But that does not mean that this cannot be done, nor that it shouldn't (I myself would be very critical of such endeavors, but that does not mean they are pointless or futile). 

I am adding a ppaer that demonstrates how researchers apply qualitative method (purportedly phenomenology) form a positivistic perspective. The researchers of course do not mention that they work from a positivist stance (positivists do not typically reflect on premises inflecting their work), but this is clear from the work.

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theoretically, yes, when we say positivism, we are at the high abstracted level of research, positivism is a research paradigm, it deals first of all with the epistemology...there is only one objective truth...

Qualitative method, is on another methodological level... to resume you can use positivism as approach and qualitative inquiry as method, you will get not generalized results that's all (since qualitative method d o not include representative sample).

to add, it is true as Yves Costa Netto said that "strategies are not mutually exclusive" but some approach like phenomenology require precise methods of inquiry

Why not? And in testing hypotheses, why not embed qualitative and quantitative methods together in the same design?

Yes. In positivism , we can use qualitative on the ground where quantitative is dominant. For instance, you can have 3 qualitative related objectives and 1 quantitative related object. The qualitative objective will help in testing the reliability and validity of the findings. Therefore, convergent mixed kind of reserch can apply.