There can be different types of models . Statistical / conceptual etc. Grounded theory can help to develop the conceptual model which can be used to develop questions which can be latter used to develop statistical model.
You can go though my papers on the use of grounded theory approach
Arjenna, in answer to your request for processes other than GT that could be used to develop a model, I recently wrote about a model-creation method which has similarities to GT and some notable differences:
Lawley, J. (2022), "Enhancing Clean Language Interviewing With Modelling", Cairns-Lee, H., Lawley, J. and Tosey, P. (Ed.) Clean Language Interviewing, Emerald Publishing Limited, Bingley, pp. 45-59.
Yes, certainly, The grounded theory at an advanced level can construct the MODEL as a procedural theory to describe and explain the reality that deals with a pragmatic process of the phenomenon. This type of model ought to build based on the substantive theory, which emerges as the result of grounded theory approach to data analysis, defining and explaining the nature of the phenomenon.
In my opinion, it depends on what you, precisely, want to do.
If you are interested in exploring concepts, links and various ways to enhance a conceptual framework, a strong and critical literature review is often enough (this Article Adhésion au plan de soins : repenser le parcours du patient ...
, for example, is based on literature and other previous qualitative research.
On the other hand, if you don't find anything in literature and you want to build a theory based on people perceptions, on a phenomenon, then two ways are possible:
Phenomenology may be used to describe such phenomenon. In fact, it's a good point of start to answer your research question.
Grounded theory will be more useful if some articles are already existing or if you want to deeply explore all the aspects of the phenomenon to build a theory that can be, afterwhile, verified by quantitative methods.
In summary:
If you need to explore links and build a model based on your context ==> literature review seems to be enough.
If you need to build a local theory on a phenomenon topic such as feelings, needs, experiences, expectations, then I would recommend you use phenomenology (or ethnology for a more community-based point of view).
If you need to build a general theory that may lead to quantitative methods, then carry on a grounded theory (be careful, it's time consuming).
A model is an extended hypothesis. What do you want to explain with the model? Cause and effect? A variable A consists of variables B, C and D? It is not so much the question of whether GT can make a model as such, as it is a question of whether GT can form the basis of what you are trying to explain. A model is just a thought construction that you can either describe in words or put into an image/graph/diagram etc.