You can do it with some javascript code.

You must fetch the templates with a REST call ( Get Available Site Templates in SharePoint using REST API  ) and then use the results on the dropdown list.

Your reply is helpful to display site templates on the Nintex form. What I am looking for is how to tie the selection from the form to the Template dropdown in the Create site action. There is no insert reference available with that drop down and i do not see Template variable available that i can use. Is there a way other then performing some scripting actions on it?

Kauser Tambawalla‌ - 

Keep in mind that this suggested solution is based off of Site Creation Workflow  that I created.

Based off of what we already spoke about, here is what I proposed:

There are two ways to do it:
1. Add actions to the workflow and update the eTemplate] workflow variable
      a. This merely requires you to add the extra choices to the variable and then add in a switch statement to evaluate the variable
      b. You will need to add in a branch of logic for each template
2. Use web services
      a. Build your association data once (the oTemplate] variable will be used, no need for multiple actions)
      b. You will still need to update the wTemplate] variable for all possible options.

I attached the .nwf file for the first option as it is the easiest to replicate and put together (but tedious if there are many options). The attached file will provide an example where there are three options (Team Site, Blank Site, and Publishing Site). You can add in more states for each template you want to make available. You then simply copy the Create Site action and update the template within the action.

I am still exploring how to setup the form to automatically pull in the available templates using web services and if I can get it working I will share

Thanks and hope this helps!