I believe that it could be either approach - I have postgraduate students that have developed a conceptual model via both approaches, and some also used a mixed method.
The terms quantitative and qualitative research are more applicable to the analysis of data rather than the creation of an artefact. If you subsequently wish to validate or evaluate the artefact you have designed then you could use either of these approaches.
I am trying to understand your question but note that the role of qualitative research is to develop theories or models and the duty of quantitative research is to test those models. Grounded theory design is there to facilitate theory development
Design Science Research (DSR) is a research paradigm, on the same level as behavioral research. A paradigm guides the decision regarding methodology, which dictates the logic behind the selection of methods.
Qualitative or quantitative addresses the level of methodology. Thus, the terms can not be used to describe design science research.
To make an example, you can build an artifact and evaluate it via expert interviews (qualitative) or via a field-test with surveys and performance monitoring (quantitative) - it depends on your problem, resources, and expected contribution.
For further reading, I would suggest the following articles:
Crotty, M. (1998). Foundations of Social Research - Meaning and Perspective in the Research Process (First Edit). Sage Publications Ltd.
Orlikowski, W. J., & Baroudi, J. J. (1991). Studying Information Technology in Organizations: Research Approaches and Assumptions. Information Systems Research, 2(1), 1–28.
Goldkuhl, G. (2012). Pragmatism vs interpretivism in qualitative information systems research. European Journal of Information Systems, 135–146.
Iivari, J. (2015). Distinguishing and Contrasting two Strategies for Design Science Research. European Journal of Information Systems, 24(1), 107–115.
If I have understood you properly you are indicating or hinting that there is no empirical data as well as analysis of empriical data in a qualitative study or research. Am I correct? After getting your answer I will be able to make a proper comment of your answer.